Random conformal dynamical systems

Abstract

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group), or almost surely a long composition of maps contracts exponentially a ball. We deduce some results about the unique ergodicity.

61 pages

References in corpus (2)

• Sur la dynamique unidimensionnelle en régularité intermédiaire
• Polymorphisms, Markov processes, random perturbations of K-automorphisms

Cited by in corpus (2)

• Unique Ergodicity of Harmonic Currents on Singular Foliations of P2
• Riemann Surface Laminations with Singularities