A directional uniformity of periodic point distribution and mixing

Pages: 1181 - 1189, Volume 30, Issue 4, August 2011

doi:10.3934/dcds.2011.30.1181       Abstract        References        Full Text (381.7K)       Related Articles

Richard Miles - School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom (email)
Thomas Ward - School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom (email)

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.

Keywords:  Rate of mixing, equidistribution of periodic points, directional uniformity, commuting transformations.
Mathematics Subject Classification:  Primary: 37C25, 37C40, 37C35.

Received: July 2010;      Revised: November 2010;      Published: May 2011.

 References