Book contents
- Frontmatter
- Contents
- Preface
- 1 Origins
- 2 Basic ideas
- 3 Finite groups
- 4 The classical groups
- 5 Compact groups
- 6 Isometry groups
- 7 Groups of integer matrices
- 8 Real homeomorphisms
- 9 Circle homeomorphisms
- 10 Formal power series
- 11 Real diffeomorphisms
- 12 Biholomorphic germs
- References
- List of frequently used symbols
- Index of names
- Subject index
- References
References
Published online by Cambridge University Press: 05 June 2015
Book contents
- Frontmatter
- Contents
- Preface
- 1 Origins
- 2 Basic ideas
- 3 Finite groups
- 4 The classical groups
- 5 Compact groups
- 6 Isometry groups
- 7 Groups of integer matrices
- 8 Real homeomorphisms
- 9 Circle homeomorphisms
- 10 Formal power series
- 11 Real diffeomorphisms
- 12 Biholomorphic germs
- References
- List of frequently used symbols
- Index of names
- Subject index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Reversibility in Dynamics and Group Theory , pp. 261 - 274Publisher: Cambridge University PressPrint publication year: 2015
References
[1] 2005. The homogeneous spectrum problem in ergodic theory. Invent. Math., 160(2), 417–446.CrossRefGoogle Scholar
[2] 2005. A complete classification for pairs of real analytic curves in the complex plane with tangential intersection. J. Dyn. Control Syst., 11(1), 1–71.CrossRefGoogle Scholar
, and [3] 2009. Reversible biholomorphic germs. Comput. Methods Funct. Theory, 9(2), 473–484.CrossRefGoogle Scholar
, and [4] 1998. Several complex variables and Banach al-gebras. Third edn. Graduate Texts in Mathematics, vol. 35. New York: Springer-Verlag.Google Scholar
, and [5] 2011. Introduction to Banach spaces and algebras. Oxford Graduate Texts in Mathematics, vol. 20. Oxford: Oxford University Press. Prepared for publication and with a preface by .Google Scholar
[6] 1962. On homeomorphisms as products of conjugates of a given homeomorphism and its inverse. Pages 231–234 of: Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961). Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
[7] 1951. On an example of a measure preserving transformation which is not conjugate to its inverse. Proc. Japan Acad., 27, 517–522.CrossRefGoogle Scholar
[8] 1984. Reversible systems. Pages 1161–1174 of: Nonlinear and turbulent processes in physics, Vol. 3 (Kiev, 1983). Chur: Harwood Academic Publ.Google Scholar
[9] 1988. Geometrical methods in the theory of ordinary differential equations. Second edn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250. New York: Springer-Verlag. Translated from the Russian by .Google Scholar
[10] 2006. Ordinary differential equations. Universitext. Berlin: Springer-Verlag. Translated from the Russian by , Second printing of the 1992 edition.Google Scholar
[11] 1968. Ergodic problems of classical mechanics. Translated from the French by . , Inc., New York-Amsterdam.Google Scholar
, and [13] 2000. Finite group theory. Second edn. Cambridge Studies in Advanced Mathematics, vol. 10. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
, , and
[15] 1997. Reversing symmetry group of Gl(2, Z) and PGl(2, Z) matrices with connections to cat maps and trace maps. J. Phys. A, 30(5), 1549–1573.CrossRefGoogle Scholar
, and [16] 2001. Symmetries and reversing symmetries of toral automorphisms. Nonlinearity, 14(4), R1–R24.CrossRefGoogle Scholar
, and [17] 2003. Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form. Phys. A, 317(1–2), 95–112.Google Scholar
, and [18] 2005. Symmetries and reversing symmetries of polynomial automorphisms of the plane. Nonlinearity, 18(2), 791–816.CrossRefGoogle Scholar
, and [19] 2006. The structure of reversing symmetry groups. Bull. Austral. Math. Soc., 73(3), 445–459.CrossRefGoogle Scholar
, and [20] 2008. Periodic orbits of linear endomorphisms on the 2-torus and its lattices. Nonlinearity, 21(10), 2427–2446.CrossRefGoogle Scholar
, , and [21] 2013. Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices. Discrete Contin. Dyn. Syst., 33(2), 527–553.Google Scholar
, , and [22] 1987. On sets of elements of the same order in the alternating group An. Publ. Math. Debrecen, 34(3–4), 313–315.Google Scholar
[23] 2002. Matrix groups. Springer Undergraduate Mathematics Series. London: Springer-Verlag London Ltd. An introduction to Lie group theory.CrossRefGoogle Scholar
[24] 1962. Permutable power series and regular iteration. J. Austral. Math. Soc., 2, 265–294.CrossRefGoogle Scholar
1961/[25] 1964. Fractional iteration near a fixpoint of multiplier 1. J. Austral. Math. Soc., 4, 143–148.CrossRefGoogle Scholar
[26] 1967. Non-embeddable functions with a fixpoint of multiplier 1. Math. Z., 99, 377–384.CrossRefGoogle Scholar
[27] 1977/78. Products of involutory matrices. I. Linear and Multi-linear Algebra, 5(1), 53–62.
[28] 1983. The geometry of discrete groups. Graduate Texts in Mathematics, vol. 91. New York: Springer-Verlag.CrossRefGoogle Scholar
[29] 1991. Ergodic theory, symbolic dynamics, and hyperbolic spaces. Oxford Science Publications. New York: The Clarendon Press Oxford University Press. Papers from the Workshop on Hyperbolic Geometry and Ergodic Theory held in Trieste, April 17–28, 1989, Edited by , and .
, , and (eds). [30] 1975. Selected topics in infinite-dimensional topology. Warsaw: PWN-Polish Scientific Publishers. Monografie Matematy-czne, Tom 58. [Mathematical Monographs, Vol. 58].Google Scholar
, and [31] 1915. The restricted problem of three bodies. Rend. Circ. Mat. Palermo, 39, 265–334.CrossRefGoogle Scholar
[32] 1939. Déformations analytiques etfonctions auto-équivalentes. Ann. Inst. H. Poincare, 9, 51–122.Google Scholar
[33] 1965. Differentiable manifolds in complex Euclidean space. Duke Math. J., 32, 1–21.CrossRefGoogle Scholar
[34] 1966. Number theory. Translated from the Russian by . Pure and Applied Mathematics, Vol. 20. New York: Academic Press.Google Scholar
, and [35] 2009. A unification of some matrix factorization results. Linear Algebra Appl., 431(10), 1719–1725.CrossRef
[36] 1963. Representations of finite groups. Pages 133–175 of: Lectures on Modern Mathematics, Vol. I. New York: Wiley.Google Scholar
[37] 2004. Every mapping class group is generated by 6 involutions. J. Algebra, 278(1), 187–198.
, and [38] 1996. The chameleon groups of Richard J. Thompson: automorphisms and dynamics. Inst. Hautes Etudes Sci. Publ. Math., 84, 5–33 (1997).CrossRefGoogle Scholar
[39] 1985. Groups of piecewise linear homeomor-phisms of the real line. Invent. Math., 79(3), 485–498.CrossRefGoogle Scholar
, and [40] 2001. Presentations, conjugacy, roots, and centralizers in groups of piecewise linear homeomorphisms of the real line. Comm. Algebra, 29(10), 4557–4596.CrossRefGoogle Scholar
, and [41] 2004. Topics from one-dimensional dynamics. London Mathematical Society Student Texts, vol. 62. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
, and [42] 1972. On approximation theory and functional equations. J. Ap-proximation Theory, 5, 228–237. Collection of articles dedicated to on his 75th birthday, III (Proc. Internat. Conf. Approximation Theory, Related Topics and their Applications, Univ. Maryland, College Park, Md., 1970).Google Scholar
[44] 1997. Products of symmetries in unitary groups. Linear Algebra Appl., 260, 9–42.CrossRefGoogle Scholar
, , and [45] 1971. Reversible homeomorphisms of the real line. Pacific J. Math., 39, 79–87.CrossRefGoogle Scholar
[46] 2000. The Nottingham group. Pages 205–221 of: New horizons in pro-p groups. Progr. Math., vol. 184. Boston, MA: Birkhauser Boston.Google Scholar
[47] 1996. Introductory notes on Richard Thompson's groups. Enseign. Math. (2), 42(3–4), 215–256.Google Scholar
, , and [48] 1993. Complex dynamics. Universitext: Tracts in Mathematics. New York: Springer-Verlag.CrossRefGoogle Scholar
, and [49] 1995. Elementary theory of analytic functions of one or several complex variables. New York: Dover Publications Inc. Translated from the French, Reprint of the 1973 edition.Google Scholar
[51] 1978. Rational quadratic forms. London Mathematical Society Monographs, vol. 13. London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers].Google Scholar
[52] 1968. Normal forms of local diffeomorphisms on the real line. Duke Math. J., 35, 549–555.CrossRefGoogle Scholar
[53] 1978. A classical invitation to algebraic numbers and class fields. New York: Springer-Verlag. With two appendices by Olga Taussky: “Artin's 1932 Gottingen lectures on class field theory” and “Connections between algebraic number theory and integral matrices”, Universitext.CrossRefGoogle Scholar
[54] 1980. Advanced number theory. New York: Dover Publications Inc. Reprint of it A second course in number theory, 1962, Dover Books on Advanced Mathematics.Google Scholar
[55] 2003. Basic algebra. London: Springer-Verlag London Ltd. Groups, rings and fields.
[56] 1994. The theorem of Kerékjártó on periodic homeomorphisms of the disc and the sphere. Enseign. Math. (2), 40(3–4), 193204.Google Scholar
, and [57] 1997. The sensual (quadratic) form. Carus Mathematical Monographs, vol. 26. Washington, DC: Mathematical Association of America. With the assistance of Francis .Google Scholar
[58] 1999. Sphere packings, lattices and groups. Third edn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290. New York: Springer-Verlag. With additional contributions by E. , , , and .CrossRefGoogle Scholar
, and [62] 1984. Linear algebra. Fourth edn. Undergraduate Texts in Mathematics. New York: Springer-Verlag. An introductory approach.CrossRefGoogle Scholar
[63] de 1993. One-dimensional dynamics. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 25. Berlin: Springer-Verlag.CrossRefGoogle Scholar
, and van [65] De 2001. Eva Kallin's lemma on polynomial convexity. Bull. London Math. Soc., 33(1), 1–10.CrossRefGoogle Scholar
[66] 1976. Reversible diffeomorphisms and flows. Trans. Amer. Math. Soc., 218, 89–113.CrossRefGoogle Scholar
[67] 1951. On the automorphisms of the classical groups. With a sup-plement by Loo-Keng Hua. Mem. Amer. Math. Soc., 1951(2), vi+122.Google Scholar
[68] 2006. On the group of homeomorphisms of the real line that map the pseudoboundary onto itself. Canad. J. Math., 58(3), 529–547.CrossRefGoogle Scholar
, and van [69] 1951. On the approximation of a function of several variables by the sum of functions of fewer variables. Pacific J. Math., 1, 195–210.CrossRefGoogle Scholar
, and [71] 1986. Pairs of involutions in the general linear group. J. Algebra, 100(1), 214–223.Google Scholar
, and
[73] 1975. Théorie itérative: introduction a latheorie des invariants holomorphes. J. Math. Pures Appl. (9), 54, 183–258.
[74] 1981. Transverse foliations of Seifert bundles and self-homeomorphism of the circle. Comment. Math. Helv., 56(4), 638–660.CrossRefGoogle Scholar
, , and [75] 1977. Bireflectionality in classical groups. Canad. J. Math., 29(6), 1157–1162.CrossRefGoogle Scholar
[77] 1993. The reflection length of a transformation in the unitary group over a finite field. Linear and Multilinear Algebra, 35(1), 11–35.CrossRefGoogle Scholar
[78] 1999. Bireflectionality of orthogonal and symplectic groups of characteristic 2. Arch. Math. (Basel), 73(6), 414–418.CrossRefGoogle Scholar
[79] 2004. Conjugacy classes of involutions in the Lorentz group Q(V) and in SO(V). Linear Algebra Appl., 383, 77–83.CrossRefGoogle Scholar
[80] 1990. Products of reflections in the kernel of the spinorial norm. Geom. Dedicata, 36(2–3), 279–285.CrossRefGoogle Scholar
, and [81] 1982. Bireflectionality of orthogonal and symplectic groups. Arch. Math. (Basel), 39(2), 113–118.CrossRefGoogle Scholar
, and [82] 2004. The special orthogonal group is trireflectional. Arch. Math. (Basel), 82(2), 122–127.CrossRefGoogle Scholar
, and [83] 2000. One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics, vol. 194. New York: Springer-Verlag. With contributions by , , , , , , , , and .Google Scholar
, and [84] 2002. Collisions and singularities in the n-body problem. Lecture Notes in Physics, vol. 590. Berlin: Springer-Verlag. Edited by and .Google Scholar
[85] 1970. A note on the Brauer-Speiser theorem. Proc. Amer. Math. Soc., 25, 620–621.CrossRefGoogle Scholar
, and
[88] 1982. Reality properties of conjugacy classes in spin groups and symplectic groups. Pages 239–253 of: Algebraists' homage: papers in ring theory and related topics (New Haven, Conn., 1981). Contemp. Math., vol. 13. Providence, R.I.: Amer. Math. Soc.Google Scholar
, and [89] 1955. On the group of homeomorphisms of an arc. Ann. of Math. (2), 62, 237–253.CrossRefGoogle Scholar
, and [90] 2006. On twisted subgroups and Bol loops of odd order. Rocky Mountain J. Math., 36(1), 183–212.CrossRefGoogle Scholar
, , and [91] 2011. The conjugacy problem in ergodic theory. Ann. of Math. (2), 173(3), 1529–1586.CrossRefGoogle Scholar
, , and [92] 1992. A smooth holomorphically convex disc in C2 that is not locally polynomially convex. Proc. Amer. Math. Soc., 116(2), 411–415.Google Scholar
[93] 2010. Strongly real elements in finite simple orthogonal groups. Sibirsk. Mat. Zh., 51(2), 241–248.Google Scholar
[94] 1990. Several complex variables. I. Encyclopaedia of Mathematical Sciences, vol. 7. Berlin: Springer-Verlag. Introduction to complex analysis, A translation of Sovremennye problemy matematiki. Fundamentalnye napravleniya, Tom 7, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. In-form., Moscow, 1985 [MR0850489 (87f:32003)], Translation by , Translation edited by .
(ed). [95] 1986. Disquisitiones arithmeticae. New York: Springer-Verlag. Translated and with a preface by Arthur , Revised by , Cornelius Greither and and with a preface by Waterhouse.CrossRefGoogle Scholar
[97] 1980. Stabilite et conjugaison differentiable pour certains feuilletages. Topology, 19(2), 179–197.CrossRefGoogle Scholar
, and [98] 2006. Classification of continuously transitive circle groups. Geom. Topol., 10, 1319–1346.CrossRefGoogle Scholar
, and [99] 2010. Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Math., 79(1–2), 23–37.CrossRefGoogle Scholar
, and [100] 2011a. Real and strongly real classes in PGLn(q) and quasi-simple covers of PSLn(q). J. Group Theory, 14, 461–489.Google Scholar
, and , and
[102] 2009. Reversibility in the group of homeomorphisms of the circle. Bull. Lond. Math. Soc., 41(5), 885–897.CrossRefGoogle Scholar
, , and [103] 2003. Reversible polynomial automorphisms of the plane: the involutory case. Phys. Lett. A, 312(1–2), 49–58.CrossRefGoogle Scholar
, and [104] 2004. Reversors and symmetries for polynomial automorphisms of the complex plane. Nonlinearity, 17(3), 975–1000.CrossRefGoogle Scholar
, and [106] 2012. Reversible complex hyperbolic isometries. Preprint.
, and [107] 1996. Transformations conjugate to their inverses have even essential values. Proc. Amer. Math. Soc., 124(9), 2703–2710.CrossRefGoogle Scholar
, and . [108] 1996. The structure of ergodic transformations conjugate to their inverses. Pages 369–385 of: Ergodic theory of Zd actions (Warwick, 1993–1994). London Math. Soc. Lecture Note Ser., vol. 228. Cambridge: Cambridge Univ. Press.Google Scholar
[109] 1997. The inverse-similarity problem for real orthogonal matrices. Amer. Math. Monthly, 104(3), 223–230.CrossRefGoogle Scholar
[110] 1999. Inverse conjugacies and reversing symmetry groups. Amer. Math. Monthly, 106(1), 19–26.CrossRefGoogle Scholar
[111] 2000a. Conjugacies between ergodic transformations and their inverses. Colloq. Math., 84/85(, part 1), 185–193. Dedicated to the memory of Anzelm Iwanik.CrossRefGoogle Scholar
[112] 2000b. The converse of the inverse-conjugacy theorem for unitary operators and ergodic dynamical systems. Proc. Amer. Math. Soc., 128(5), 1381–1388.CrossRefGoogle Scholar
[113] 2002. Ergodic dynamical systems conjugate to their composition squares. Acta Math. Univ. Comenian. (N.S.), 71(2), 201–210.Google Scholar
[114] 2010. Groups having elements conjugate to their squares and connections with dynamical systems. Applied Mathematics, 1, 416–424.CrossRefGoogle Scholar
[115] 1996. Ergodic transformations conjugate to their inverses by involutions. Ergodic Theory Dynam. Systems, 16(1), 97–124.CrossRefGoogle Scholar
, del , , and [116] 2007. Spectral properties of ergodic dynamical systems conjugate to their composition squares. Colloq. Math., 107(1), 99–118.CrossRefGoogle Scholar
[118] 1975. Real-valued characters of solvable groups. Bull. London Math. Soc., 7, 132.CrossRefGoogle Scholar
[119] 1976. Real-valued characters and the Schur index. J. Algebra, 40(1), 258–270.CrossRefGoogle Scholar
[120] 1979. Real-valued and 2-rational group characters. J. Algebra, 61(2), 388–413.CrossRefGoogle Scholar
[121] 1981. Products of two involutions in classical groups of characteristic 2. J. Algebra, 71(2), 583–591.CrossRefGoogle Scholar
[122] 1988. Commutators in the symplectic group. Arch. Math. (Basel), 50(3), 204–209.CrossRefGoogle Scholar
[123] 2001. Simeadracht amchulaithe chorais dinimiciuil. in: , and (eds), Proceedings of the Irish Systems and Signals Conference, 27–31. Translation available online from AOF.Google Scholar
, , and [124] 1997. Diagram groups. Mem. Amer. Math. Soc., 130(620), viii+117.
, and [125] 1991. On products of involutions. Pages 237–255 of: Paul Halmos. New York: Springer.Google Scholar
[126] 1976. Products of involutions. Linear Algebra andAppl., 13(1/2), 157–162. Collection of articles dedicated to Olga Taussky Todd.Google Scholar
, , and [127] 1942. Operator methods in classical me-chanics. II. Ann. of Math. (2), 43, 332–350.CrossRefGoogle Scholar
, and von [128] 1998. Every group has a terminating transfinite automorphism tower. Proc. Amer. Math. Soc., 126(11), 3223–3226.CrossRefGoogle Scholar
[129] 1974. Finitely presented infinite simple groups. Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra. Notes on Pure Mathematics, No. 8 (1974).Google Scholar
[130] 2007. Automorphisms of finite abelian groups. Amer. Math. Monthly, 114(10), 917–923.CrossRefGoogle Scholar
, and [131] 1974. Differential equations, dynamical systems, and linear algebra. Academic Press [A subsidiary of Harcourt Brace Jo-vanovich, Publishers], New York-London. Pure and Applied Mathematics, Vol. 60.Google Scholar
, and [132] 2000. Classification and orbit equivalence relations. Mathematical Surveys and Monographs, vol. 75. Providence, RI: American Mathematical Society.Google Scholar
[133] 2001. Products of roots of the identity. Proc. Amer. Math. Soc., 129(2), 459–465.CrossRefGoogle Scholar
, , and [134] 1971. Products of two involutions in the general linear group. Indiana Univ. Math. J., 20, 1017–1020.CrossRefGoogle Scholar
, and 1970/[135] 1998. On an n-manifold in Cn near an elliptic complex tangent. J. Amer. Math. Soc., 11(3), 669–692.CrossRefGoogle Scholar
, and
[137] 1993. Nonlinear Stokes phenomena. Pages 1–55 of: Nonlinear Stokes phenomena. Adv. Soviet Math., vol. 14. Providence, RI: Amer. Math. Soc.CrossRefGoogle Scholar
[138] 1976. Character theory of finite groups. New York: Academic Press [Harcourt Brace Jovanovich Publishers]. Pure and Applied Mathematics, No. 69.Google Scholar
[139] 1995. Involutary expressions for elements in GLn(Z) and SLn(Z). Linear Algebra Appl., 219, 165–177.CrossRefGoogle Scholar
[140] 2001. Representations and characters of groups. Second edn. New York: Cambridge University Press.CrossRefGoogle Scholar
, and [141] 2002. Reversible interval homeomorphisms. J. Math. Anal. Appl., 272(2), 473–479.CrossRefGoogle Scholar
, , and
[143] 1915. Conformal classification of analytic arcs or elements: Poincaré's local problem of conformal geometry. Trans. Amer. Math. Soc., 16(3), 333–349.Google Scholar
[144] 1916. Infinite Groups Generated by Conformal Transformations of Period Two (Involutions and Symmetries). Amer. J. Math., 38(2), 177–184.CrossRefGoogle Scholar
[145] 1995. Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge: Cambridge University Press. With a supplementary chapter by Katok and Leonardo Mendoza.CrossRefGoogle Scholar
, and [146] Strongly real special 2-groups. To appear.
, and [147] 1982. The local hull of holomorphy of a surface in the space of two complex variables. Invent. Math., 67(1), 1–21.CrossRefGoogle Scholar
, and [149] 1988. Products of involutions in orthogonal groups. Pages 231–247 of: Combinatorics '86 (Trento, 1986). Ann. Discrete Math., vol. 37. Amsterdam: North-Holland.Google Scholar
[150] 1987a. On products of two involutions in the orthogonal group of a vector space. Linear Algebra Appl., 94, 209–216.CrossRefGoogle Scholar
, and [151] 1987b. Products of involutions in O+(V). Linear Algebra Appl., 94, 217–222.CrossRefGoogle Scholar
, and , and
[153] 1998. Involutions and commutators in orthogonal groups. J. Austral. Math. Soc. Ser. A, 65(1), 1–36.CrossRefGoogle Scholar
, and [154] 2005. On strong reality of finite simple groups. Acta Appl. Math., 85(1–3), 195–203.CrossRefGoogle Scholar
, and [155] 1970. Commuting diffeomorphisms. Pages 165–184 of: Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968). Providence, R.I.: Amer. Math. Soc.Google Scholar
[156] 2005. On stable torsion length of a Dehn twist. Math. Res. Lett., 12(2–3), 335–339.CrossRefGoogle Scholar
[157] 1990. Iterative functional equations. Encyclopedia of Mathematics and its Applications, vol. 32. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
, , and [159] 1992. Reversing symmetries in dynamical systems. J. Phys. A, 25(4), 925–937.CrossRefGoogle Scholar
[161] 1996. Area-preserving dynamics that is not reversible. Phys. A, 228(1–4), 344–365.CrossRefGoogle Scholar
[162] 1994. Reversing k-symmetries in dynamical systems. Phys. D, 73(4), 277–304.CrossRefGoogle Scholar
, and [163] 1995. Cyclic reversing k-symmetry groups. Nonlinearity, 8(6), 1005–1026.CrossRefGoogle Scholar
, and [164] 1998. Time-reversal symmetry in dynamical systems: a survey. Phys. D, 112(1–2), 1–39. Time-reversal symmetry in dynamical systems (Coventry, 1996).Google Scholar
, and [165] 1993. Conditions for local (reversing) symmetries in dynamical systems. Phys. A, 197(3), 379–422.CrossRefGoogle Scholar
, , and [166] 2007. Reversible maps in the group of quaternionic Möbius transformations. Math. Proc. Cambridge Philos. Soc., 143(1), 57–69.CrossRefGoogle Scholar
, , and . , , , and
[169] 1988a. Decomposition of matrices into three involutions. Linear Algebra Appl., 111, 1–24.CrossRefGoogle Scholar
[170] 1988b. Decomposition of matrices into three involutions. Linear Algebra Appl., 111, 1–24.CrossRefGoogle Scholar
[171] 1974/75. Fractional iteration near a fix point of multiplier 1. J. London Math. Soc. (2), 9, 599–609.Google Scholar
[173] 1993. Renormalisation in area-preserving maps. Advanced Series in Nonlinear Dynamics, vol. 6. River Edge, NJ: World Scientific Publishing Co. Inc.CrossRefGoogle Scholar
[174] 1982. Travaux d'Écalle et de Martinet-Ramis sur les systemes dynamiques. Pages 59–73 of: Bourbaki Seminar, Vol. 1981/1982. Astérisque, vol. 92. Paris: Soc. Math. France.Google Scholar
[175] 1970. Homeomorphisms of the circle without periodic points. Proc. London Math. Soc. (3), 20, 688–698.Google Scholar
, and
[177] 1983. Approximation by a sum of two algebras. The lightning bolt principle. J. Funct. Anal., 52(3), 353–368.CrossRefGoogle Scholar
, and [178] 2014. The Kourovka notebook. Eighteenth edn. Novosibirsk: Russian Academy of Sciences Siberian Division Institute of Mathematics. Unsolved problems in group theory, Including archive of solved problems.
, and (eds). [179] 1985. The classification of the conjugacy classes of the full group of homeomorphisms of an open interval and the general solution of certain functional equations. Proc. London Math. Soc. (3), 51(1), 95–112.Google Scholar
, and [180] 1978. Groups of homeomorphisms with manageable automorphism groups. Comm. Algebra, 6(5), 497–528.Google Scholar
[181] 1992. Refutation of a theorem of Diliberto and Straus. Mat. Zametki, 51(4), 78–80, 142.Google Scholar
[182] 1981. Every power series is a Taylor series. Amer. Math. Monthly, 88(1), 51–52.CrossRefGoogle Scholar
[183] 1971. On group-theoretic decision problems and their classification. Princeton, N.J.: Princeton University Press. Annals of Mathematics Studies, No. 68.Google Scholar
[184] 1983. Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations. Acta Math., 150(3–4), 255–296.CrossRefGoogle Scholar
, and [185] 1961. Automorphisms of formal power series under substitution. Trans. Amer. Math. Soc., 99, 373–383.CrossRefGoogle Scholar
[186] 1998. The classification of curvilinear angles in the complex plane and the groups of ± holomorphic diffeomorphisms. Ann. Fac. Sci. Toulouse Math. (6), 7(2), 313–334.CrossRefGoogle Scholar
[187] 2007. Grupos de difeomorfismos del círculo. Ensaios Matemáticos [Mathematical Surveys], vol. 13. Rio de Janeiro: Sociedade Brasileira de Matematica.Google Scholar
[188] 2004. Conjugacy, involutions, and reversibility for real homeomorphisms. Irish Math. Soc. Bull., 54, 41–52.Google Scholar
[189] 2008. Composition of involutive power series, and reversible series. Comput. Methods Funct. Theory, 8(1–2), 173–193.Google Scholar
[190] 2010. Conjugacy of real diffeomorphisms. Asurvey. Algebra i Analiz, 22(1), 3–56.Google Scholar
, and , and
[192] 2009. Reversibility in the diffeomorphism group of the real line. Publ. Mat., 53(2), 401–415.Google Scholar
, and [193] Formally-reversible maps of (ℂ2,0). To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), DOI:10.2422/2036–2145.201201_001.
, and [194] 2014. Factoring formal maps into reversible or involutive factors. J. Algebra, 399, 657–674.Google Scholar
, and [195] 1995. Nonlinearizable holomorphic dynamics having an uncountable number of symmetries. Invent. Math., 119(1), 67–127.Google Scholar
[196] 1907. Les fonctions analytiques de deux variables et la prepresentation conforme. Rend. Circ. Mat. Palermo, 23(1), 185–220.CrossRefGoogle Scholar
[197] 1996. Œuvres. Tome VI. Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics]. Sceaux: Éditions Jacques Gabay. Géométrie. Analysis situs (topologie). [Geometry. Analysis situs (topology)], Reprint of the 1953 edition.
[198] 1989. Local reversibility in dynamical systems. Phys. Lett. A, 142(2–3), 112–116.CrossRefGoogle Scholar
, and , and
[200] 1975. Decomposition of matrices into simple involutions. Linear Algebra and Appl., 12(3), 247–255.CrossRefGoogle Scholar
[201] 1981. The group generated by involutions. Proc. Roy. Irish Acad. Sect. A, 81(1), 9–12.Google Scholar
[202] 2011. Strongly real elements of orthogonal groups in even characteristic. J. Group Theory, 14(1), 9–30.CrossRefGoogle Scholar
[203] 1994. Foundations of hyperbolic manifolds. Graduate Texts in Mathematics, vol. 149. New York: Springer-Verlag.CrossRefGoogle Scholar
[204] 1992. Area preserving mappings that are not reversible. Phys. Lett. A, 162(3), 243–248.CrossRefGoogle Scholar
, and [205] 1992. Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems. Phys. Rep., 216(2–3), 63–177.CrossRefGoogle Scholar
, and [206] 1996. A course in the theory of groups. Second edn. Graduate Texts in Mathematics, vol. 80. New York: Springer-Verlag.CrossRefGoogle Scholar
[207] 2007. Reciprocal geodesics. Pages 217–237 of: Analytic number theory. Clay Math. Proc., vol. 7. Providence, RI: Amer. Math. Soc.Google Scholar
[208] 1933. Über die Permutationsgruppe der naturlichen Zahlenfolge. StudiaMath., 4, 134–141.Google Scholar
, and [209] 2007. Compact Lie groups. Graduate Texts in Mathematics, vol. 235. New York: Springer.CrossRefGoogle Scholar
[210] 1985. The geometry of Markoff numbers. Math. Intelligencer, 7(3), 20–29.CrossRefGoogle Scholar
[211] 1986. Reversible systems. Lecture Notes in Mathematics, vol. 1211. Berlin: Springer-Verlag.CrossRefGoogle Scholar
[212] 2009. Word maps, conjugacy classes, and a noncommutative Waring-type theorem. Ann. of Math. (2), 170(3), 1383–1416.CrossRefGoogle Scholar
. [213] 2008. Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space. Math. Proc. R. Ir. Acad., 108(1), 33–46.CrossRefGoogle Scholar
[214] 1995. Lectures on Celestial Mechanics, reprint of the 1971 edition. Berlin, Heidelberg: Springer.Google Scholar
, and [215] 1996. Representations of finite and compact groups. Graduate Studies in Mathematics, vol. 10. Providence, RI: American Mathematical Society.Google Scholar
[216] 2005. Reality properties of conjugacy classes in G2. Israel J. Math., 145, 157–192.CrossRefGoogle Scholar
, and [217] 2008. Reality properties of conjugacy classes in algebraic groups. Israel J. Math., 165, 1–27.CrossRefGoogle Scholar
, and [218] 1974. Regular elements of finite reflection groups. Invent. Math., 25, 159–198.CrossRefGoogle Scholar
[219] 1972. Conjugacy separability of groups of integer matrices. Proc. Amer. Math. Soc., 32, 1–7.CrossRefGoogle Scholar
[220] 1957. Local Cn transformations of the real line. Duke Math. J., 24, 97–102.CrossRefGoogle Scholar
[221] 1986. Uniform separation of points and measures and representation by sums of algebras. Israel J. Math., 55(3), 350–362.CrossRefGoogle Scholar
[222] 1979. Algebraic number theory. London: Chapman and Hall. Chapman and Hall Mathematics Series.CrossRefGoogle Scholar
, and [223] 1964. Fractional iteration of entire and rational functions. J. Austral. Math. Soc., 4, 129–142.CrossRefGoogle Scholar
[224] 1973. Normal forms for certain singularities of vectorfields. Ann. Inst. Fourier (Grenoble), 23(2), 163–195. Colloque International sur l'Analyse et la Topologie Differentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972).CrossRefGoogle Scholar
[225] 1992. The geometry of the classical groups. Sigma Series in Pure Mathematics, vol. 9. Berlin: Heldermann Verlag.Google Scholar
[226]
The automorphism tower problem. Book in preparation.[227] 1985. The automorphism tower problem. Proc. Amer. Math. Soc., 95(2), 166–168.CrossRefGoogle Scholar
[228] 1961. Commutators in the special and general linear groups. Trans. Amer. Math. Soc., 101, 16–33.CrossRefGoogle Scholar
[229] 1962a. Commutators of matrices with coefficients from the field of two elements. Duke Math. J., 29, 367–373.Google Scholar
[231] 2005. Real conjugacy classes in algebraic groups and finite groups of Lie type. J. Group Theory, 8(3), 291–315.CrossRefGoogle Scholar
, and [232] 2003. Discrimination analytique des difféomorphismes résonnants de (ℂ,0) et réflexion de Schwarz. Astérisque, 271–319. Autour de l'analyse microlocale.Google Scholar
[233] 2010. Strong reality of finite simple groups. Sibirsk. Mat. Zh., 51(4), 769–777.Google Scholar
, and [234] 2003. An example of a bireflectional spin group. Arch. Math. (Basel), 81(1), 1–4.CrossRefGoogle Scholar
[235] 2004. A factorization in GSp(V). Linear Multilinear Algebra, 52(6), 385–403.CrossRefGoogle Scholar
[236] 1981. Analytic classification of germs of conformal mappings (C, 0) → (C, 0). Funktsional. Anal. i Prilozhen., 15(1), 1–17, 96.CrossRefGoogle Scholar
[237] 1982. Analytic classification of pairs of involutions and its applications. Funktsional. Anal. i Prilozhen., 16(2), 21–29, 96.CrossRefGoogle Scholar
[238] 1963. On the conjugacy classes in the unitary, symplectic and orthogonal groups. J. Austral. Math. Soc., 3, 1–62.CrossRefGoogle Scholar
[239] 1999. The dynamics of circle homeomorphisms: a hands-on introduction. Math. Mag., 72(1), 3–13.CrossRefGoogle Scholar
[240] 1996. Double valued reflection in the complex plane. Enseign. Math. (2), 42(1–2), 25–48.Google Scholar
[241] 1997. A note on extremal discs and double valued reflection. Pages 271–276 of: Multidimensional complex analysis and partial differential equations (Sao Carlos, 1995). Contemp. Math., vol. 205. Providence, RI: Amer. Math. Soc.Google Scholar
[242] 1998. Real ellipsoids and double valued reflection in complex space. Amer. J. Math., 120(4), 757–809.CrossRefGoogle Scholar
[243] 1997. The classical groups. Princeton Landmarks in Mathematics. Princeton, NJ: Princeton University Press. Their invariants and representations, Fifteenth printing, Princeton Paperbacks.Google Scholar
[244] 1963. On isomorphic groups and homeomorphic spaces. Ann. of Math. (2), 78, 74–91.CrossRefGoogle Scholar
[245] 1995. Local polynomially convex hulls at degenerated CR singularities of surfaces in C2. Indiana Univ. Math. J., 44(3), 897–915.CrossRefGoogle Scholar
[246]
, , , , , , , , , and ATLAS of finitie group representations – Version3. http://brauer.maths.qmul.ac.uk/Atlas/v3/.[247] 1966. Transformations which are products of two involutions. J. Math. Mech., 16, 327–338.Google Scholar
[248] 1992. The existence of noncollision singularities in Newtonian systems. Ann. of Math. (2), 135(3), 411–468.CrossRefGoogle Scholar
[249] 1966. Automorphisms of the complex numbers. Math. Magazine, 39, 135–141.CrossRefGoogle Scholar
[250] 1995. Petits diviseurs en dimension 1. Paris: Société Mathématique de France. Astérisque No. 231 (1995).Google Scholar
[251] 1994. The representation of homeomorphisms on the interval as finite compositions of involutions. Proc. Amer. Math. Soc., 121(2), 605–610.CrossRefGoogle Scholar