Almost strong mixing group actions in topological dynamics

2014/05/23 by Jane Wang, Wang, Jane
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1405.5971

22 pages, 1 figure

arxiv created 2014/05/23 · arxiv updated 2014/05/26

Abstract

In ergodic theory, given sufficient conditions on the system, every weak mixing ℕ-action is strong mixing along a density one subset of ℕ. We ask if a similar statement holds in topological dynamics with density one replaced with thickness. We show that given sufficient initial conditions, a group action in topological dynamics is strong mixing on a thick subset of the group if and only if the system is k-transitive for all k, and conclude that an analogue of this statement from ergodic theory holds in topological dynamics when dealing with abelian groups.

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