A directional uniformity of periodic point distribution and mixing

R Miles, T Ward

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3 Citations (Scopus)

Abstract

For mixing [\mathbb Z^d] -actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure supported on periodic points to Haar measure occurs at a uniform rate independent of the direction.
Original languageEnglish
Pages (from-to)1181-1189
Number of pages9
JournalDiscrete and Continuous Dynamical Systems
Volume30
Issue number4
DOIs
Publication statusPublished - Aug 2011

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