Article contents
The structure of pointwise recurrent maps having the pseudo orbit tracing property
Published online by Cambridge University Press: 22 January 2016
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We show that a continuous map of a metric space is pointwise recurrent and has the pseudo orbit tracing property if and only if the map is uniformly conjugate to an adding-machine-like map restricted to some invariant subset.
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 2002
References
[A]
Aoki, N., Homeomorphisms without the pseudo orbit tracing property, Nagoya Math. J., 88 (1982), 155–160.Google Scholar
[AH]
Aoki, N. and Hiraide, K., Topological theory of dynamical systems, Elsevier Science B.V., Netherland, 1994.Google Scholar
[CKY]
Coven, E., Kan, I. and Yorke, J., Pseudo-orbit shadowing in the family of tent maps, Trans. Amer. Math. Soc., 308 (1988), 227–241.Google Scholar
[K]
Kuchta, M., Shadowing property of continuous maps with zero topological entropy, Proc. Amer. Math. Soc., 119 (1993), 641–648.Google Scholar
[KP]
Kolev, B. and Peroueme, M.-C., Recurrent surface homeomorphism, Math. Proc. Camb. Phil. Soc., 124 (1998), 161–168.Google Scholar
[KW]
Katznelson, Y. and Weiss, B., When all points are recurrent/generic, Ergodic Theory and Dynamical Systems I (College Park, 1979–80) (A. Katok, ed.), Progr. Math. 10, Birkhauser Verlag, Boston (1981), pp. 195–210.Google Scholar
[M]
Mai, J. H., Pointwise recurrent dynamical systems with pseudo orbit tracing property, Northeast Math. J., 12 (1996), 73–78.Google Scholar
[OT]
Oversteegen, L. G. and Tymchatyn, E. D., Recurrent homeomorphisms on 2 are periodic, Proc. Amer. Math. Soc., 110 (1990), 1083–1087.Google Scholar
[PP]
Yu, S.. Pilyugin, S. and Plamenevskaya, O. B., Shadowing is generic, Topology Appl., 97 (1999), 253–266.Google Scholar
- 14
- Cited by