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A NOTE ON WEAK EXPANSIVE HOMEOMORPHISMS ON A COMPACT METRIC SPACE

  • Koo, Namjip (Department of Mathematics, Chungnam National University) ;
  • Tumur, Gansukh (Department of Mathematics, Mongolian National University of Education)
  • Received : 2020.01.14
  • Accepted : 2020.01.21
  • Published : 2020.02.15

Abstract

In this paper we introduce the notion of the expansivity for homeomorphisms on a compact metric space and study some properties concerning weak expansive homeomorphisms. Also, we give some examples to illustrate our results.

Keywords

References

  1. M. Achigar, A. Artigue, and I. Monteverde, Expansive homeomorphisms on non-Hausdorff spaces, Topology Appl., 207 (2016), 109-122. https://doi.org/10.1016/j.topol.2016.04.016
  2. J. Ahn and S. Kim, Stability of weak measure expansive diffeomorphisms, J. Korean Math. Soc., 55 (2018), no. 5, 1131-1142. https://doi.org/10.4134/JKMS.J170607
  3. W. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures, Monatsh Math., 79 (1975), 81-92. https://doi.org/10.1007/BF01585664
  4. R. Bowen, Entropy-expansive maps, Trans. Amer. Math. Soc., 164 (1972), 323-331. https://doi.org/10.1090/S0002-9947-1972-0285689-X
  5. H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math., 45 (1993), no. 3, 576-598. https://doi.org/10.4153/CJM-1993-030-4
  6. C. A. Morales, Measure-expansive systems, preprint, IMPA Serie D, 2011.
  7. C. A. Morales, A generalization of expansivity, Discrete Contin. Dyn. Syst., 32 (2012), no. 1, 293-301. https://doi.org/10.3934/dcds.2012.32.293
  8. W. R. Utz, Unstable homeomorphisms, Proc. Amer. Math. Soc., 1 (1950), no. 6, 769-774. https://doi.org/10.1090/S0002-9939-1950-0038022-3