English

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.

Keywords

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