Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T00:45:22.082Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffeomorphisms with the shadowing property

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Kazuhiro Sakai
Kazuhiro Sakai
Affiliation:
Department of Mathematics Kanagawa University Rokkakubashi Kanagawa-ku Yokohama 221 Japan e-mail: [email protected]
Rights & Permissions [Opens in a new window]

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.

It is proved that for every diffeomorphism f on a surface satisfying Axiom A, f is in the C2-interior of the set of all diffeoomorphisms having the shadowing property if and only if f satisfies the strong transversality condition.

Keywords

Axiom Abasic setshadowing property

MSC classification

Secondary: 54H20: Topological dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 396 - 399
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]de Melo, W., ‘Structural stability of diffeomorphisms on two-manifolds’, Invent. Math. 21 (1973), 233–246.Google Scholar
[2]Moriyasu, K., ‘The topological stability of diffeomorphisms’, Nagoya Math. J. 123 (1991), 91–102.CrossRefGoogle Scholar
[3]Newhouse, S., ‘The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms’, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 101–151.Google Scholar
[4]Palis, J. and de Melo, W., Geometric theory of dynamical systems (an introduction) (Springer, Berlin, 1982).CrossRefGoogle Scholar
[5]Robinson, C., ‘Structural stability of C 1 diffeomorphisms’, J. Differential Equations 22 (1976), 28–73.CrossRefGoogle Scholar
[6]Robinson, C., ‘Stability theorems and hyperbolicity in dynamical systems’, Rocky Mountain J. Math. 7 (1977), 425–437.CrossRefGoogle Scholar
[7]Sakai, K., ‘Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds’, Osaka J. Math. 31 (1994), 373–386.Google Scholar
[8]Sakai, K., ‘Shadowing property and transversality condition’, in: Proceedings of the International Conference on Dynamical Systems and Chaos in Tokyo 1994, vol. 1 (World Scientific, Singapore, 1995) pp. 233–238.Google Scholar