Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonstandard Expansiveness   Let $(X,d)$ be a metric space and $f: X \rightarrow X$ be a homeomorphism. We
say that a dynamical system $(X,f)$ is \emph{expansive}, with constant of
expansivity $c \in \mathbb{R{^+}}$, if for all $x,y \in X$ , $x \neq y$, exists
$n \in \mathbb{Z}$, 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 $x,y \in X$, if $x\neq y$ then the set $\lbrace n \in
\mathbb{Z} : d(f^n(x), f^n(y) > c \rbrace$ is infinite.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom