Year: 2025
Type: preprint
Abstract: We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if the topological entropy of the map is zero, then the chain recurrent set is finite; (3) the map has only finitely many chain components; (4) if the space is perfect, then the topological entropy of the map is positive; and (5) if the space is connected, then the map is locally eventually onto and hence mixing. Several examples are also provided.
Source: arXiv (Cornell University)
Author: Kawaguchi, Noriaki
Institution: Tokyo Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415348212
Cites:
Cited by:
Related to: