English

Unique ergodicity for zero-entropy dynamical systems with the approximate product property

Dynamical Systems 2020-07-03 v3

Abstract

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.

Keywords

Cite

@article{arxiv.1908.01149,
  title  = {Unique ergodicity for zero-entropy dynamical systems with the approximate product property},
  author = {Peng Sun},
  journal= {arXiv preprint arXiv:1908.01149},
  year   = {2020}
}

Comments

15 pages, final version

R2 v1 2026-06-23T10:38:50.144Z