Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some variational principles for the metric mean dimension of a semigroup
  action   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}.

31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin