English

Relative topological entropy and relative mean dimension of induced factors

Dynamical Systems 2025-11-25 v1

Abstract

We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we prove that a factor map has zero relative topological entropy if and only if so does the induced factor map. On the other hand, we prove that a factor map has positive relative topological entropy if and only if the induced factor map has infinite relative mean dimension.

Keywords

Cite

@article{arxiv.2511.18040,
  title  = {Relative topological entropy and relative mean dimension of induced factors},
  author = {Kairan Liu and Yixiao Qiao},
  journal= {arXiv preprint arXiv:2511.18040},
  year   = {2025}
}