Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-21T09:04:33.359Z Has data issue: false hasContentIssue false

Bianchi Cosmologies as Dynamical Systems

Published online by Cambridge University Press:  12 April 2016

Andrzej J. Maciejewski
Affiliation:
Toruń Centre for Astronomy, N. Copernicus University, Chopina 12/18, 87-100 Toruń, Poland; E-mail:maciejka@astri.uni.torun.pl
Marek Szydłowski
Affiliation:
Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Kraków, Poland; E-mail:uoszydlo@cyf-kr.edu.pl

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss specific properties of dynamical systems originating from cosmology and relativity. In particular, we present results of our study of the Bianchi class A cosmological models. We introduce new variables in which the Hamiltonian constraint for all the class A models is solved algebraically. We present results of dimension reduction of the investigated models.

Type
Cosmology
Copyright
Copyright © Kluwer 1999

References

Landau, L.D. and Lifshitz, E.M.: 1975, The Classical Theory of Fields. Pergamon, Oxford.Google Scholar
Wainwright, J. and Ellis, G.F.R.: 1997, Dynamical Systems in Cosmology, Cambridge, U.P., Cambridge.CrossRefGoogle Scholar
Collins, C.B.: 1971 Commun. Math. Phys., 23, 137 (1971).CrossRefGoogle Scholar
Bogoyavlensky, O.I.: 1985, Methods in Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics. New York, Springer-Verlag.Google Scholar
Wainwright, J. and Hsu, L.: 1989 Class. Quantum Grav., 6, 1409.CrossRefGoogle Scholar
Chernoff, D.F. and Barrow, J.D.: 1983, Phys. Rev. Lett., 20, (1983), 134137.CrossRefGoogle Scholar
Cushman, R. and Śniatycki, J.: 1995, Preprint Univ. of Calgary,.Google Scholar
Cornish, N.J.: 1997, in Proceedings of Eight M. Grossmann Meeting, Jerusalem.Google Scholar
Cornish, N.J. and Levin, J.J.: 1997, in Proceedings of Eight M. Grossmann Meeting, Jerusalem.Google Scholar
Ramani, A., Grammaticos, B. and Bountis, T.: 1989, Phys. Reports 180, 159254.CrossRefGoogle Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1993, J. Phys., A26, 5795.Google Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1994, J. Phys. A, 27, 53575361.CrossRefGoogle Scholar
Latifi, A.,Musette, M. and Conte, R.: 1995, Phys. Lett. A, 194, 8397.CrossRefGoogle Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1995, J. Phys. A, 28, 53135322.CrossRefGoogle Scholar
Morales-Ruiz, J.J. and Ramis, J.-P.: 1997, Galoisian Obstruction to Integrability of Hamiltonian Systems I, II, Preprint.Google Scholar
Belinskii, V. A., Khalatnikov, I.M. and Lifshitz, E. M.: 1982, Adv. Phys., 31, 639.CrossRefGoogle Scholar
Maciejewski, A. J. and Szydłowski, M.: 1998, J. Phys. A. Math. & Gen., 31, 2031.CrossRefGoogle Scholar