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.
@article{bwmeta1.element.bwnjournal-article-apmv63z2p183bwm, author = {Masatoshi Oka}, title = {Pseudo orbit tracing property and fixed points}, journal = {Annales Polonici Mathematici}, volume = {63}, year = {1996}, pages = {183-186}, zbl = {0849.58050}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z2p183bwm} }
Masatoshi Oka. Pseudo orbit tracing property and fixed points. Annales Polonici Mathematici, Tome 63 (1996) pp. 183-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z2p183bwm/
[000] [1] R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319. | Zbl 0127.13102
[001] [2] R. Bowen, Entropy-expansive maps, Trans. Amer. Math. Soc. 164 (1972), 323-331. | Zbl 0229.28011
[002] [3] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. | Zbl 0212.29201
[003] [4] M. Dateyama, Homeomorphisms with the pseudo orbit tracing property of the Cantor set, Tokyo J. Math. 6 (1983), 287-290. | Zbl 0533.58019
[004] [5] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976. | Zbl 0328.28008
[005] [6] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, 1948.
[006] [7] M. Misiurewicz, Diffeomorphisms without any measure with maximal entropy, Bull. Acad. Polon. Sci. 21 (1973), 903-910. | Zbl 0272.28013
[007] [8] A. Morimoto, The method of pseudo-orbit tracing and stability of dynamical systems, Seminar note 39, University of Tokyo, 1979 (in Japanese).
[008] [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. | Zbl 0691.54026