A directional uniformity of periodicpoint distribution and mixing

Richard Miles; Thomas Ward

doi:10.3934/dcds.2011.30.1181

Article Contents

2011, Volume 30, Issue 4: 1181-1189. Doi: 10.3934/dcds.2011.30.1181

This issue Previous Article Some remarks for a modified periodic Camassa-Holm system Next Article New entropy conditions for scalar conservation laws with discontinuous flux

A directional uniformity of periodic point distribution and mixing

Richard Miles^1, and
Thomas Ward^1,

1.
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ

Received: June 30, 2010

Revised: October 31, 2010

Published: September 2011

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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.

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Mathematics Subject Classification: Primary: 37C25, 37C40, 37C35.

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