METRIC ENTROPY OF HOMEOMORPHISM ON NON-COMPACT METRIC SPACE  

作　　者：周云华 

机构地区：[1]College of Mathematics and Statistics, Chongqing University

出　　处：《Acta Mathematica Scientia》2011年第1期102-108,共7页数学物理学报（B辑英文版）

基　　金：supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)

摘　　要：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.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.

关 键 词：Topological entropy metric entropy non-compact metric space one point compactification 

分 类 号：O189.11[理学—数学] O189.1[理学—基础数学]