Random conformal dynamical systems

Details Random conformal dynamical systems Random conformal dynamical systems

2005-06-10

arxiv.org/abs/math/0506204v1

Geom. Funct. Anal. 17 no. 4 (2007) 1043-1105

Mathematics

Dynamical Systems

61 pages

Scientific paper

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.

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