Topic
Oseledets theorem
About: Oseledets theorem is a research topic. Over the lifetime, 16 publications have been published within this topic receiving 304 citations.
Papers
TL;DR: In this paper, it was shown that the Lyapunov exponents of volume preserving diffeomorphisms of a compact manifold are continuous if and only if the Oseledets splitting is either dominated or trivial.
Abstract: We show that the Lyapunov exponents of volume preserving C 1 diffeomor- phisms of a compact manifold are continuous at a given diffeomorphism if and only if the Os- eledets splitting is either dominated or trivial. It follows that for a C 1 -residual subset of volume preserving diffeomorphisms the Oseledets splitting is either dominated or trivial. We obtain analogous results in the setting of symplectic diffeomorphisms, where the conclusion is actually stronger: dominated splitting is replaced by partial hyperbolicity. We also obtain versions of these results for continuous cocycles with values in some matrix groups. In the text we give the precise statements of these results and the ideas of the proofs. The complete proofs will appear in (4). 2002 Editions scientifiques et medicales Elsevier SAS AMS classification: 37C40; 37A35; 7A20 RESUME. - Nous montrons que les exposants de Lyapunov des diffeomorphismes de classe C 1 qui preservent le volume dans une variete compacte sont continus a un diffeomorphisme donne si et seulement si sa decomposition de Oseledets est dominee ou bien triviale. Il s'en suit que pour un sous-ensemble C 1 -residuel des diffeomorphismes qui preservent le volume, la decomposition
45 citations
Book•
1 Jan 1991
TL;DR: In this article, Lyapunov exponents and invariant measures for nonlinear stochastic differential equations have been derived for random dynamical systems on grassmannians, where Lyapounov functions have been shown to have almost sure exponential stability.
Abstract: Random dynamical systems.- Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Lyapunov exponents of random dynamical systems on grassmannians.- Eigenvalue representation for the Lyapunov exponents of certain Markov processes.- Analytic dependence of Lyapunov exponents on transition probabilities.- A second order extension of Oseledets theorem.- The upper Lyapunov exponent of Sl(2,R) cocycles: Discontinuity and the problem of positivity.- Linear skew-product flows and semigroups of weighted composition operators.- Filtre de Kalman Bucy et exposants de Lyapounov.- Invariant measures for nonlinear stochastic differential equations.- How to construct stochastic center manifolds on the level of vector fields.- Additive noise turns a hyperbolic fixed point into a stationary solution.- Lyapunov functions and almost sure exponential stability.- Large deviations for random expanding maps.- Multiplicative ergodic theorems in infinite dimensions.- Stochastic flow and lyapunov exponents for abstract stochastic PDEs of parabolic type.- The Lyapunov exponent for products of infinite-dimensional random matrices.- Lyapunov exponents and complexity for interval maps.- An inequality for the Ljapunov exponent of an ergodic invariant measure for a piecewise monotonic map of the interval.- Generalisation du theoreme de Pesin pour l'?-entropie.- Systems of classical interacting particles with nonvanishing Lyapunov exponents.- Lyapunov exponents from time series.- Lyapunov exponents in stochastic structural dynamics.- Stochastic approach to small disturbance stability in power systems.- Lyapunov exponents and invariant measures of equilibria and limit cycles.- Sample stability of multi-degree-of-freedom systems.- Lyapunov exponents of control flows.
14 citations
TL;DR: In this paper, a semi-invertible Oseledets theorem for nonlinear cocycles acting on measurable fields of Banach spaces was proved for the first time.
Abstract: We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for nonlinear cocycles acting on measurable fields of Banach spaces.
12 citations
TL;DR: In this paper, it was shown that the subbundles given by Oseledets Theorem are Hoelder-continuous on compact sets of measure arbitrarily close to 1.
Abstract: For Hoelder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hoelder-continuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmueller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmueller disk.
11 citations
1 Jan 1991
5 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2019 | 2 |
| 2018 | 1 |
| 2016 | 1 |
| 2015 | 1 |
| 2014 | 2 |