METRIC ENTROPY OF HOMEOMORPHISM ON NON-COMPACT METRIC SPACE

Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊...

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Published in:Acta mathematica scientia 2011, Vol.31 (1), p.102-108
Main Author: 周云华
Format: Article
Language:English
Subjects:
37A05
37A35
Entropy
metric entropy
Metric space
non-compact metric space
one point compactification
Topological entropy
Topology
一致连续
局部紧
拓扑熵
熵理论
紧度量空间
紧致度量空间
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description Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.
doi_str_mv 10.1016/S0252-9602(11)60212-9
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subjects 37A05
37A35
Entropy
metric entropy
Metric space
non-compact metric space
one point compactification
Topological entropy
Topology
一致连续
局部紧
拓扑熵
熵理论
紧度量空间
紧致度量空间
title METRIC ENTROPY OF HOMEOMORPHISM ON NON-COMPACT METRIC SPACE
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