Miles, Richard; Ward, Thomas A directional uniformity of periodic point distribution and mixing. (English) Zbl 1219.37019 Discrete Contin. Dyn. Syst. 30, No. 4, 1181-1189 (2011). Summary: 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. Cited in 2 Documents MSC: 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C35 Orbit growth in dynamical systems Keywords:rate of mixing; equidistribution of periodic points; directional uniformity; commuting transformations PDFBibTeX XMLCite \textit{R. Miles} and \textit{T. Ward}, Discrete Contin. Dyn. Syst. 30, No. 4, 1181--1189 (2011; Zbl 1219.37019) Full Text: DOI arXiv