Nonstandard Expansiveness

arXiv2101.00498MaRDI QIDQ6357440

Author name not available (Why is that?)

Publication date: 2 January 2021

Abstract: Let $(X,d)$ be a metric space and $f:XightarrowX$ be a homeomorphism. We say that a dynamical system $(X,f)$ is emph{expansive}, with constant of expansivity $cinmathbbR{}^{+}$, if for all $x,yinX$ , $xeqy$, exists $ninmathbbZ$, such that $d(f^n(x),f^n(y))>c$. In this paper we will use the theory of Nonstandard Analysis to study a subfamily of these dynamics, which verify that for all $x,yinX$, if $xeqy$ then the set $lbraceninmathbbZ:d(f^n(x),f^n(y)>cbrace$ is infinite.

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