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On the virtual automorphism group of a minimal flow

Part of: Topological dynamics Connections with other structures, applications

Published online by Cambridge University Press:  07 February 2020

JOSEPH AUSLANDER  and
ELI GLASNER
JOSEPH AUSLANDER
Affiliation:
Mathematics Department, The University of Maryland, College Park, MD 20742, USA email jna@math.umd.edu
ELI GLASNER
Affiliation:
Department of Mathematics, Tel Aviv University, Tel Aviv, Israel email glasner@math.tau.ac.il
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Abstract

We introduce the notions ‘virtual automorphism group’ of a minimal flow and ‘semiregular flow’ and investigate the relationship between the virtual and actual group of automorphisms.

Keywords

semiregular minimal flowEllis groupMorse minimal setautomorphism group

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 54H20: Topological dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 5 , May 2021 , pp. 1281 - 1295
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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References

Auslander, J.. Regular minimal sets. I. Trans. Amer. Math. Soc. 123 (1966), 469–479.CrossRefGoogle Scholar
Auslander, J.. Minimal Flows and Their Extensions (North-Holland Mathematics Studies, 153) . North-Holland, Amsterdam, 1988.Google Scholar
Auslander, J. and Glasner, S.. Distal and highly proximal extensions of minimal flows. Indiana Univ. Math. J. 26 (1977), 731–749.CrossRefGoogle Scholar
Cortez, M. I. and Petite, S.. On the centralizers of minimal aperiodic actions on the Cantor set. Preprint, 2018, arXiv:1807.04654.Google Scholar
de Vries, J.. Elements of Topological Dynamics. Kluwer Academic Publishers, Dordrecht, 1993.CrossRefGoogle Scholar
Downarowicz, T.. The royal couple conceals their mutual relationship: a noncoalescent Toeplitz flow. Israel J. Math. 97 (1997), 239–251.CrossRefGoogle Scholar
Ellis, R.. Lectures on Topological Dynamics. W. A. Benjamin, New York, 1969.Google Scholar
Ellis, R., Glasner, E. and Shapiro, L.. Proximal-isometric flows. Adv. Math. 17 (1975), 213–260.CrossRefGoogle Scholar
Glasner, S.. Proximal Flows (Lecture Notes in Mathematics, 517) . Springer, Berlin, 1976.CrossRefGoogle Scholar
Glasner, S.. Regular PI metric flows are equicontinuous. Proc. Amer. Math. Soc. 114 (1992), 269–277.CrossRefGoogle Scholar
Glasner, E. and Megrelishvili, M.. Hereditarily non-sensitive dynamical systems and linear representations. Colloq. Math. 104 (2006), 223–283.CrossRefGoogle Scholar
Glasner, E., Tsankov, T., Weiss, B. and Zucker, A.. Bernoulli disjointness. Preprint, 2019, arXiv:1901.03406.Google Scholar
Gottschalk, W. H. and Hedlund, G. A.. Topological Dynamics (AMS Colloquium Publications, 36) . American Mathematical Society, Providence, RI, 1955.CrossRefGoogle Scholar
Haddad, K. N. and Johnson, S. A.. Recurrent sequences and IP sets, II, Iberoamerican Conference on Topology and its Applications (Morelia, 1997). Topology Appl. 98 (1999), 203–210.CrossRefGoogle Scholar
Horelick, B.. Pointed minimal sets and S-regularity. Proc. Amer. Math. Soc. 20 (1969), 150–156.Google Scholar
Kellendonk, J. and Yassawi, R.. The Ellis semigroup of bijective substitutions, Preprint, 2019, arXiv:1908.05690.Google Scholar
Mackey, G. W.. Ergodic theory and virtual groups. Math. Ann. 166 (1966), 187–207.CrossRefGoogle Scholar
Parry, W. and Walters, P.. Minimal skew-product homeomorphisms and coalescence. Compos. Math. 22 (1970), 283–288.Google Scholar
Staynova, P.. The Ellis semigroup of certain constant-length substitutions. Ergod. Th. & Dynam. Sys. to appear.Google Scholar
Veech, W. A.. Topological dynamics. Bull. Amer. Math. Soc. 83 (1977), 775–830.CrossRefGoogle Scholar
Zimmer, R. J.. Extensions of ergodic actions and generalized discrete spectrum. Bull. Amer. Math. Soc. 81 (1975), 633–636.CrossRefGoogle Scholar
Zucker, A.. A direct solution to the generic point problem. Proc. Amer. Math. Soc. 146 (2018), 2143–2148.CrossRefGoogle Scholar
Zucker, A.. Minimal flows with arbitrary centralizer. Preprint, 2019, arXiv:1909.08394.Google Scholar