ArticleOriginal scientific text

Title

Pseudo orbit tracing property and fixed points

Authors 1

Affiliations

  1. Department of Mathematics, Science University of Tokyo, Noda-shi, Chiba-ken, 278 Japan

Abstract

If a continuous map f of a compact metric space has the pseudo orbit tracing property and is h-expansive then the set of all fixed points of f is totally disconnected.

Keywords

pseudo orbit tracing property, h-expansive

Bibliography

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  3. R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414.
  4. M. Dateyama, Homeomorphisms with the pseudo orbit tracing property of the Cantor set, Tokyo J. Math. 6 (1983), 287-290.
  5. M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976.
  6. W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, 1948.
  7. M. Misiurewicz, Diffeomorphisms without any measure with maximal entropy, Bull. Acad. Polon. Sci. 21 (1973), 903-910.
  8. A. Morimoto, The method of pseudo-orbit tracing and stability of dynamical systems, Seminar note 39, University of Tokyo, 1979 (in Japanese).
  9. T. Shimomura, On a structure of discrete dynamical systems from the view point of chain components and some applications, Japan. J. Math. 15 (1989), 99-126.
Pages:
183-186
Main language of publication
English
Received
1995-02-10
Published
1996
Exact and natural sciences