Ergodicity and mixing of noncommuting epimorphisms

V Bergelson, A Gorodnik

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

Abstract

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.
Translated title of the contributionErgodicity and mixing of noncommuting epimorphisms
Original languageEnglish
Pages (from-to)329 - 359
Number of pages31
JournalProceedings of the London Mathematical Society
Volume95 (2)
DOIs
Publication statusPublished - Sep 2007

Bibliographical note

Publisher: Oxford University Press

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