Random conformal dynamical systems
Dynamical Systems
2011-12-30 v1 Probability
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.
Cite
@article{arxiv.math/0506204,
title = {Random conformal dynamical systems},
author = {Bertrand Deroin and Victor Kleptsyn},
journal= {arXiv preprint arXiv:math/0506204},
year = {2011}
}
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61 pages