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A directional uniformity of periodic point distribution and mixing

Miles, R.; Ward, T.

A directional uniformity of periodic point distribution and mixing Thumbnail


Authors

R. Miles

T. Ward



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.

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