ﻻ يوجد ملخص باللغة العربية
In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapiras entropy related to finite open covers. Second we establish a variational principle in terms of Katoks entropy. Finally using these two variational principles we develop a variational principle in terms of Brin-Katok local entropy.
In this article, we introduce a notion of relative mean metric dimension with potential for a factor map $pi: (X,d, T)to (Y, S)$ between two topological dynamical systems. To link it with ergodic theory, we establish four variational principles in te
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov-Lindenstrauss-Weiss mean dimensions for actions of countable amenable groups, and are useful for distinguishing co
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension sy
We introduce an invariant, called mean rank, for any module M of the integral group ring of a discrete amenable group $Gamma$, as an analogue of the rank of an abelian group. It is shown that the mean dimension of the induced $Gamma$-action on the Po
Associated to a IFS one can consider a continuous map $hat{sigma} : [0,1]times Sigma to [0,1]times Sigma$, defined by $hat{sigma}(x,w)=(tau_{X_{1}(w)}(x), sigma(w))$ were $Sigma={0,1, ..., d-1}^{mathbb{N}}$, $sigma: Sigma to Sigma$ is given by$sigma(