A directional uniformity of periodic point distribution and mixing

Details A directional uniformity of periodic point distribution and mixing A directional uniformity of periodic point distribution and mixing

2010-01-03

arxiv.org/abs/1001.0390v2

Mathematics

Dynamical Systems

Scientific paper

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.

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