A directional uniformity of periodic point distribution and mixing

Miles, R.; Ward, T.

Abstract

For mixing 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.

Citation

Miles, R., & Ward, T. (2011). A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems - Series A, 30(4), 1181-1189. https://doi.org/10.3934/dcds.2011.30.1181

• Journal Article Type: Article
• Publication Date: Aug 1, 2011
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Oct 16, 2012
• Journal: Discrete and Continuous Dynamical Systems - Series A
• Print ISSN: 1078-0947
• Electronic ISSN: 1553-5231
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 4
• Pages: 1181-1189
• DOI: https://doi.org/10.3934/dcds.2011.30.1181
• Keywords: Rate of mixing, Equidistribution of periodic points, Directional uniformity, Commuting transformations.
• Public URL: https://durham-repository.worktribe.com/output/1495489