×

A directional uniformity of periodic point distribution and mixing. (English) Zbl 1219.37019

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.

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
PDFBibTeX XMLCite
Full Text: DOI arXiv