The structure of pointwise recurrent expansive homeomorphisms
Dynamical Systems
2022-01-04 v1
Abstract
Let be a compact metric space and let be a homeomorphism on . We show that if is both pointwise recurrent and expansive, then the dynamical system is topologically conjugate to a subshift of some symbolic system. Moreover, if is pointwise positively recurrent, then the subshift is semisimple; a counterexample is given to show the necessity of positive recurrence to ensure the semisimilicity.
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}
}