Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T13:48:36.172Z Has data issue: false hasContentIssue false

Stochastic stability of hyperbolic attractors

Published online by Cambridge University Press:  19 September 2008

Lai-Sang Young
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
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.

We study the effects of small random errors on the asymptotic distribution of points in the basin of a hyperbolic attractor.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[B]Bowen, R.. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math, Vol. 470, Springer-Verlag (1975).CrossRefGoogle Scholar
[BR]Bowen, R. & Ruelle, D.. The ergodic theory of Axiom A flows. Invent. Math. 29 (1975), 181202.CrossRefGoogle Scholar
[F]Franks, J.. Time dependent stable diffeomorphisms. Invent. Math. 24 (1974), 163172.CrossRefGoogle Scholar
[HP]Hirsch, M. & Pugh, C.. Stable manifolds and hyperbolic sets. AMS Proc. Symp. Pure Math. Vol. 14, (1970), 133164.CrossRefGoogle Scholar
[K1]Kifer, Y.. On small random perturbations of some smooth dynamical systems. Math. USSR Izvestija 8 (1974) 10831107.CrossRefGoogle Scholar
[K2]Kifer, Y.. General random perturbations of hyperbolic and expanding transformations. Preprint.Google Scholar
[PS]Pugh, C. & Shub, M.. Ergodicity of Anosov actions. Invent. Math. 15 (1972) 123.CrossRefGoogle Scholar
[Sh]Shub, M.. Stabilité globale des systemes dynamiques. Asterisque vol. 56 (1978). (English translation by J. Christy to appear.)Google Scholar
[Si]Sinai, Ya. G.. Markov partitions and C-diffeomorphisms. Func. Anal. and its Appl. 2 (1968), No. 1, 6489.Google Scholar