Pseudo orbit tracing property and fixed points

• Autorzy: Masatoshi Oka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pseudo orbit tracing property; h-expansive

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 2
• Strony: 183-186

Daty

wydano

1996

otrzymano

1995-02-10

Twórcy

autor

Masatoshi Oka

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

Bibliografia

• [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319.
• [2] R. Bowen, Entropy-expansive maps, Trans. Amer. Math. Soc. 164 (1972), 323-331.
• [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.