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Ergodicity and mixing of non-commuting epimorphisms

Bergelson, Vitaly and Gorodnik, Alexander (2007) Ergodicity and mixing of non-commuting epimorphisms. Proceedings of the London Mathematical Society, 95 (2). pp. 329-359. ISSN 0024-6115. doi:10.1112/plms/pdm007.

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We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group X. In particular, we show that a set F, with |F| > dim X, of epimorphisms of X is mixing if and only if every subset of F of cardinality (dim X) + 1 is mixing. We also construct examples of free non-abelian groups of automorphisms of tori which are mixing, but not mixing of order 3, and show that, under some irreducibility assumptions, ergodic groups of automorphisms contain mixing subgroups and free non-abelian mixing subsemigroups.

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Additional Information:© 2007 London Mathematical Society. Received 21 December 2005; revised 18 October 2006; published online 4 April 2007. The research of the first author was partially supported by NSF grants DMS-0400631 and DMS-06007181, and that of the second author was partially supported by NSF grant DMS-0400631. We would like to thank Y. Benoist and H. Oh for helpful discussions and D. Berend, R. Pavlov, and T. Ward for useful comments about this paper.
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Issue or Number:2
Classification Code:2000 Mathematics Subject Classification 37A25, 37A15.
Record Number:CaltechAUTHORS:20091019-121230678
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16384
Deposited By: Tony Diaz
Deposited On:21 Oct 2009 17:45
Last Modified:08 Nov 2021 23:26

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