数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 102-108.doi: 10.1016/S0252-9602(11)60212-9

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METRIC ENTROPY OF HOMEOMORPHISM ON |NON-COMPACT METRIC SPACE

周云华   

  1. College of Mathematics and Statistics, Chongqing University, China
  • 收稿日期:2007-09-24 修回日期:2009-08-28 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    This work was supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)

METRIC ENTROPY OF HOMEOMORPHISM ON |NON-COMPACT METRIC SPACE

 ZHOU Yun-Hua   

  1. College of Mathematics and Statistics, Chongqing University, China
  • Received:2007-09-24 Revised:2009-08-28 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    This work was 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.

关键词: Topological entropy, metric entropy, non-compact metric space, one point compactification

Abstract:

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.

Key words: Topological entropy, metric entropy, non-compact metric space, one point compactification

中图分类号: 

  • 37A05