Pseudo orbit tracing property and fixed points

Masatoshi Oka

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 2, page 183-186
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Masatoshi Oka. "Pseudo orbit tracing property and fixed points." Annales Polonici Mathematici 63.2 (1996): 183-186. <http://eudml.org/doc/262698>.

@article{MasatoshiOka1996,
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.},
author = {Masatoshi Oka},
journal = {Annales Polonici Mathematici},
keywords = {pseudo orbit tracing property; h-expansive; -expansive map},
language = {eng},
number = {2},
pages = {183-186},
title = {Pseudo orbit tracing property and fixed points},
url = {http://eudml.org/doc/262698},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Masatoshi Oka
TI - Pseudo orbit tracing property and fixed points
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 2
SP - 183
EP - 186
AB - 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.
LA - eng
KW - pseudo orbit tracing property; h-expansive; -expansive map
UR - http://eudml.org/doc/262698
ER -

References

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  1. [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319. Zbl0127.13102
  2. [2] R. Bowen, Entropy-expansive maps, Trans. Amer. Math. Soc. 164 (1972), 323-331. Zbl0229.28011
  3. [3] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. Zbl0212.29201
  4. [4] M. Dateyama, Homeomorphisms with the pseudo orbit tracing property of the Cantor set, Tokyo J. Math. 6 (1983), 287-290. Zbl0533.58019
  5. [5] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976. Zbl0328.28008
  6. [6] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, 1948. 
  7. [7] M. Misiurewicz, Diffeomorphisms without any measure with maximal entropy, Bull. Acad. Polon. Sci. 21 (1973), 903-910. Zbl0272.28013
  8. [8] A. Morimoto, The method of pseudo-orbit tracing and stability of dynamical systems, Seminar note 39, University of Tokyo, 1979 (in Japanese). 
  9. [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. Zbl0691.54026

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