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Équilibre statistique pour les produits de difféomorphismes aléatoires indépendants (Statistical equilibrium for products of random diffeomorphisms). (French) Zbl 0589.60053

This note is concerned with properties of invariant measures of a Markov chain on a compact manifold V induced by i.i.d. diffeomorphisms. The two main assertions are: if the sum of the Lyapunov exponents associated to an invariant measure m is negative then a.s. the measure \(\mu_{\omega}\) is singular with respect to Riemannian volumes \((d\mu_{\omega}(x)dP(\omega)\) is the associated invariant measure for the skew product transformation on \(V\times \Omega)\). If furthermore the largest Lyapunov exponent is negative then a.s. \(\mu_{\omega}\) is a convex combination of Dirac measures with equal weights.
Reviewer: H.Crauel

MSC:

60H99 Stochastic analysis
37A99 Ergodic theory
58J65 Diffusion processes and stochastic analysis on manifolds
60J60 Diffusion processes
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