Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-29T00:04:16.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Consequences of the Pseudo Orbits Tracing Property and Expansiveness

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Jerzy Ombach
Jerzy Ombach
Affiliation:
Instytut Matematyki Uniwersytet Jagiellońskiul Reymonta 4, 30059 Krakow, Poland
Rights & Permissions [Opens in a new window]

Extract

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.

Let f be an expansive homeomorphism with the pseudo orbits tracing property on a compact metric space. There are stable and unstable “manifolds” with similar properties as in the hyperbolic case, and similar behavior near periodic points is observed. Per (f) = Ω(f) = CR(f). Mappings Ω and CR are continuous at f.

MSC classification

Secondary: 54H20: Topological dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 301 - 313
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bowen, R., Equilibrium states and the ergodic theory of Anosov diffeomorphisms (Lecture Notes in Math. 470(1975)).CrossRefGoogle Scholar
[2]Conley, C., Isolated invariant sets and the Morse index (Amer. Math. Soc., 1978).CrossRefGoogle Scholar
[3]Hirsch, M. and Pugh, C., ‘Stable manifolds and hyperbolic sets’, Proc. Sympos. Pure Math., Vol 14, pp. 133–164 (Amer. Math. Soc., Providence, Rhode Island, 1970).Google Scholar
[4]Hurley, M., ‘Attractors: persistence and density of their basins’, Trans. Amer. Math. Soc. 269 (1982), 247–271.CrossRefGoogle Scholar
[5]Hurley, M., ‘Bifurcation and chain recurrence’, Ergodic Theory Dynamical Systems 3 (1983), 231–240.CrossRefGoogle Scholar
[6]Hurley, M., ‘ Consequences of topological stability’, J. Differential Equations 54 (1984), 60–72.CrossRefGoogle Scholar
[7]Nitecki, Z., Differentiate dynamics (M.I.T., Cambridge, Mass., 1971).Google Scholar
[8]Shub, M., Stabilité globale des systèmes dynamiques, (Astérisque 56 (1978)).Google Scholar
[9]Walters, P., On the pseudo orbits tracing property and its relationship to stability, pp. 231–244 (Lecture Notes in Math. 668).CrossRefGoogle Scholar