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Random Conformal Dynamical Systems

Published in Geometric And Functional Analysis. 2007, vol. 17, no. 4, p. 1043 - 1105
Abstract 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.
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DEROIN, Bertrand, KLEPTSYN, Victor Alexeevitch. Random Conformal Dynamical Systems. In: Geometric and Functional Analysis, 2007, vol. 17, n° 4, p. 1043 - 1105. https://archive-ouverte.unige.ch/unige:9781

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Deposited on : 2010-07-29

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