Entropy points for amenable group actions
Abstract
In this paper, we investigate topological dynamical systems for amenable group actions and study local properties of topological entropy, particularly concerning entropy points and uniform entropy points. We present two distinct approaches to defining entropy points and introduce the concept of uniform entropy points using local entropy functions. The relationship between these two types of entropy points and the structure of their corresponding sets is systematically examined. Furthermore, we prove the existence of a countable closed subset whose entropy, computed along a fixed Følner sequence, attains the entropy of the original system.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
advanced mathematical theories
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 51
- Issue
- 0
- Pages
- 250–277
- Publication date
- 1 January 2026