Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ENTROPY MAPS FOR MEASURE EXPANSIVE HOMEOMORPHISM

  • JEONG, JAEHYUN (Department of Mathematics Chungnam National University) ;
  • JUNG, WOOCHUL (Department of Mathematics Chungnam National University)
  • Received : 2015.02.04
  • Accepted : 2015.07.22
  • Published : 2015.08.15
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Abstract

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

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References

  1. H. Keynes and J. Robertson, Gerenators for topological entropy and expansiveness, Math. Systems Theory 3 (1969), 51-59. https://doi.org/10.1007/BF01695625
  2. C. A. Morales, Partition's sensitivity for measurable maps, Mathematica Bohemica 138 (2013), 133-148.
  3. C. A. Morales, Measure-expansive systems, preprint.
  4. Ja. G. Sinai, On the concept of entropy for a dynamic system, Dokl. Akad. Nauk SSSR 124 (1959), 768-771.
  5. P. Walters, An Introduction to Ergodic Theory, Springer Verlag, 1982.