Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property

Tullio Ceccherini-Silberstein; Michel Coornaert

doi:10.1007/s10883-020-09485-3

Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property

Dynamical Systems 2024-04-05 v3

Authors: Tullio Ceccherini-Silberstein , Michel Coornaert

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Abstract

We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every pre-injective continuous self-mapping of $X$ commuting with the action of $G$ on $X$ is surjective. This extends a result previously obtained by Hanfeng Li in the case when $X$ is metrizable.

Keywords

expansive actions weak specification property myhill property amenable groups topological entropy compact hausdorff spaces

Cite

@article{arxiv.1905.02740,
  title  = {Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property},
  author = {Tullio Ceccherini-Silberstein and Michel Coornaert},
  journal= {arXiv preprint arXiv:1905.02740},
  year   = {2024}
}

Comments

We have corrected a few typos and removed part (iii) of Theorem 4.2. It is accepted for publication in the Journal of Dynamical and Control Systems

Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property

Abstract

Keywords

Cite

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