Acta mathematica scientia, Series B >
METRIC ENTROPY OF HOMEOMORPHISM ON |NON-COMPACT METRIC SPACE
Received date: 2007-09-24
Revised date: 2009-08-28
Online published: 2011-01-20
Supported by
This work was supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)
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.
ZHOU Yun-Hua . METRIC ENTROPY OF HOMEOMORPHISM ON |NON-COMPACT METRIC SPACE[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 102 -108 . DOI: 10.1016/S0252-9602(11)60212-9
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