Some variational principles for the metric mean dimension of a semigroup action
Dynamical Systems
2021-07-06 v1 Mathematical Physics
math.MP
Abstract
In this manuscript we show that the metric mean dimension of a free semigroup action satisfies three variational principles: (a) the first one is based on a definition of Shapira's entropy, introduced in \cite{SH} for a singles dynamics and extended for a semigroup action in this note; (b) the second one treats about a definition of Katok's entropy for a free semigroup action introduced in \cite{CRV-IV}; (c) lastly we consider the local entropy function for a free semigroup action and show that the metric mean dimension satisfies a variational principle in terms of such function. Our results are inspired in the ones obtained by \cite{LT2019}, \cite{VV}, \cite{GS1} and \cite{RX}.
Keywords
Cite
@article{arxiv.2107.01968,
title = {Some variational principles for the metric mean dimension of a semigroup action},
author = {Thomas Jacobus and Fagner B. Rodrigues and Marcus V. Silva},
journal= {arXiv preprint arXiv:2107.01968},
year = {2021}
}