EXPANSIVE HOMEOMORPHISMS WITH THE SHADOWING PROPERTY ON ZERO DIMENSIONAL SPACES

Title & Authors
EXPANSIVE HOMEOMORPHISMS WITH THE SHADOWING PROPERTY ON ZERO DIMENSIONAL SPACES
Park, Jong-Jin;

Abstract
Let X = {a} $\small{{\cup}}$ {$\small{a_{i}}$ ${$\small{\mid}$}$i $\small{\in}$ N} be a subspace of Euclidean space $\small{E^2}$ such that $\small{lim_{{i}{\longrightarrow}{\infty}}a_{i}}$ = a and $\small{a_{i}\;{\neq}\;a_{j}}$ for $\small{i{\neq}j}$. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} $\small{{\cup}}$ {$a_{i}{$\small{\mid}$}i{\in}Z$} is a subspace of $\small{E^2}$ such that $\small{lim_{i}}$-$\small{\infty}$ $\small{a_{i}}$ = b and $\small{lim_{{i}{\longrightarrow}{\infty}}a_{i}}$ = a with the following properties; $\small{a_{i}{\neq}a_{j}}$ for $\small{i{\neq}j}$ and $\small{a{\neq}b}$.
Keywords
expansive homeomorphism;$\small{\delta}$-pseudo-orbit;shadowing property (pseudo orbit tracing property);Dense;Zero dimensional space;
Language
English
Cited by
1.
Topological stability and pseudo-orbit tracing property for expansive measures, Journal of Differential Equations, 2016
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