Scientific article

Random Conformal Dynamical Systems

Published inGeometric and functional analysis, vol. 17, no. 4, p. 1043-1105
Publication date2007

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversally 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 pseudogroup), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.

Citation (ISO format)
DEROIN, Bertrand, KLEPTSYN, Victor Alexeevitch. Random Conformal Dynamical Systems. In: Geometric and functional analysis, 2007, vol. 17, n° 4, p. 1043–1105. doi: 10.1007/s00039-007-0606-y
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Article (Published version)
ISSN of the journal1016-443X

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