Lowering topological entropy over subsets for amenable group actions
Dynamical Systems
2026-01-29 v2
Abstract
In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is lowerable, D-lowerable, and P-lowerable, and that asymptotic h-expansiveness is equivalent to hereditary uniform lowerability. Moreover, we prove a Bowen's type theorem for amenable group actions.
Cite
@article{arxiv.2510.19613,
title = {Lowering topological entropy over subsets for amenable group actions},
author = {Xiaochen Wang},
journal= {arXiv preprint arXiv:2510.19613},
year = {2026}
}