English

The structure of pointwise recurrent expansive homeomorphisms

Dynamical Systems 2022-01-04 v1

Abstract

Let XX be a compact metric space and let f:XXf:X\rightarrow X be a homeomorphism on XX. We show that if ff is both pointwise recurrent and expansive, then the dynamical system (X,f)(X, f) is topologically conjugate to a subshift of some symbolic system. Moreover, if ff is pointwise positively recurrent, then the subshift is semisimple; a counterexample is given to show the necessity of positive recurrence to ensure the semisimilicity.

Keywords

Cite

@article{arxiv.2201.00110,
  title  = {The structure of pointwise recurrent expansive homeomorphisms},
  author = {Enhui Shi and Hui Xu and Ziqi Yu},
  journal= {arXiv preprint arXiv:2201.00110},
  year   = {2022}
}
R2 v1 2026-06-24T08:37:22.715Z