An almost mixing of all orders property of algebraic dynamical systems

L. Arenas-Carmona, D. Berend, V. Bergelson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider dynamical systems, consisting of-actions by continuous automorphisms on shift-invariant subgroups of, where is the field of order. These systems provide natural generalizations of Ledrappier's system, which was the first example of a 2-mixing-action that is not 3-mixing. Extending the results from our previous work on Ledrappier's example, we show that, under quite mild conditions (namely, 2-mixing and that the subgroup defining the system is a principal Markov subgroup), these systems are almost strongly mixing of every order in the following sense: for each order, one just needs to avoid certain effectively computable logarithmically small sets of times at which there is a substantial deviation from mixing of this order.

Original languageEnglish
Pages (from-to)1211-1233
Number of pages23
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number5
DOIs
StatePublished - 1 May 2019

Fingerprint

Dive into the research topics of 'An almost mixing of all orders property of algebraic dynamical systems'. Together they form a unique fingerprint.

Cite this