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

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.

15 pages, final version

References in corpus (1)

• Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

Cited by in corpus (2)

• Ergodic measures of intermediate entropies for dynamical systems with the approximate product property
• Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures