Hostname: page-component-cb9f654ff-w5vf4 Total loading time: 0 Render date: 2025-09-11T02:13:55.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo-orbit tracing property for random diffeomorphisms*

Published online by Cambridge University Press:  14 November 2011

Liu Peidong ,
Qian Minping  and
Tang Fuchang
Liu Peidong
Affiliation:
Department of Mathematics, Peking University, Beijing, 100871, P.R. China
Qian Minping
Affiliation:
Department of Probability and Statistics, Peking University, Beijing, 100871, P.R. China
Tang Fuchang
Affiliation:
Department of Probability and Statistics, Peking University, Beijing, 100871, P.R. China
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider the pseudo-orbit tracing property for dynamical systems generated by iterations of random diffeomorphisms. We first define a type of hyperbolicity by means of a ‘random’ multiplicative ergodic theorem, and then prove our shadowing result by employing the graph transformation methods. That result applies to, for example, the case of small random diffeomorphisms type perturbations of hyperbolic sets of deterministic dynamical systems.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1027 - 1033
Copyright
Copyright © Royal Society of Edinburgh 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Anosov, D. V.. Geodesic flows on compact Riemannian manifolds of negative curvature. Proc. Steklov Inst. Math. 90 (1967).Google Scholar
2Blank, M. L.. Metric properties of ɛ-trajectories of dynamical systems with stochastic behaviour. Ergodic Theory Dynam. Systems 8 (1988), 365–78.CrossRefGoogle Scholar
3Chow, Shui-Nee and Vleck, Eric S. Van. A shadowing lemma for random diffeomorphisms. Random Comput. Dynam. 1(2) (1992–1993), 197–218.Google Scholar
4Kifer, Y.. Ergodic Theory of Random Transformations (Boston: Birkhauser, 1986).CrossRefGoogle Scholar
5Peidong, Liu. R-stability of orbit spaces for C1 endomorphisms. Chinese Ann. Math. Ser. A 12 (1991), 415–21.Google Scholar
6Sauer, T. and Yorke, J.. Rigorous verification of trajectories for the computer simulation of dynamical systems. Nonlinearity 4 (1991), 961–79.CrossRefGoogle Scholar
7Shub, M.. Global Stability of Dynamical Systems (Berlin: Springer, 1987).CrossRefGoogle Scholar