Invariant manifolds for products of random diffeomorphisms

被引：0

作者：

Dahlke S. ^{[1
]}

机构：

[1] Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen

来源：

Journal of Dynamics and Differential Equations | 1997年 / 9卷 / 2期

关键词：

Ergodic theory; Invariant manifolds; Lyapunov exponents; Random diffeomorphisms;

D O I：

10.1007/BF02219220

中图分类号：

学科分类号：

摘要：

This paper is concerned with the construction of invariant families of submanifolds for products of random diffeomorphisms on a compact Riemannian manifold. These submanifolds can be obtained for almost arbitrary parameters disjoint from the Lyapunov spectrum of the resulting cocycle. Local measurable families are constructed and the globalization problem is discussed. We present a globalization result for generalized stable and unstable manifolds. © 1997 Plenum Publishing Corporation.

引用

页码：157 / 210

页数：53

共 20 条

[1] Abraham R., Robbin J., Transversal Mappings and Flows, (1967)
[2] Arnold L., Crauel H., Random dynamical systems, Lecture Notes in Mathematics, 1486, pp. 1-22, (1991)
[3] Boxler P., A stochastic version of center manifold theory, Prob. Th. Rel. Fields, 83, pp. 505-545, (1989)
[4] Brin M., Kifer Y., Dynamics of Markov chains and stable manifolds for random diffeomorphisms, Ergod. Theory Dynam. Syst., 7, pp. 351-374, (1987)
[5] Carr J., Applications of Center Manifold Theory, (1981)
[6] Carverhill A., Flows of stochastic dynamical systems: Ergodic theory, Stochastics, 14, pp. 273-317, (1985)
[7] Crauel H., Extremal exponents of random dynamical systems do not vanish, J. Dynam. Diff. Eq., 2, pp. 245-291, (1990)
[8] Dahlke S., Invariant Families of Submanifolds for Diffeomorphims, (1988)
[9] Dahlke S., Invariante Mannigfaltigkeiten für Produkte Zufälliger Diffeomorphismen, (1989)
[10] Fathi A., Herman M., Yoccoz J.C., Proof of Pesin's stable manifold theorem, Lecture Notes in Mathematics, 1007, pp. 177-215, (1983)

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