## 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 contribution | Ergodicity and mixing of noncommuting epimorphisms |
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Original language | English |

Pages (from-to) | 329 - 359 |

Number of pages | 31 |

Journal | Proceedings of the London Mathematical Society |

Volume | 95 (2) |

DOIs | |

Publication status | Published - Sep 2007 |