Random conformal dynamical systems

Bertrand Deroin; Victor Kleptsyn

doi:10.1007/s00039-007-0606-y

Random conformal dynamical systems

Bertrand Deroin
, Victor Kleptsyn

Université Paris-Saclay
University of Geneva
CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon
CNRS - Independent University of Moscow

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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 pseudo-group), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.

langue originale	Anglais
Pages (de - à)	1043-1105
Nombre de pages	63
journal	Geometric and Functional Analysis
Volume	17
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/s00039-007-0606-y
état	Publié - 1 nov. 2007
Modification externe	Oui

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10.1007/s00039-007-0606-y

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title = "Random conformal dynamical systems",

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 pseudo-group), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.",

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AU - Kleptsyn, Victor

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AB - 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 pseudo-group), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.

KW - Brownian motion

KW - Conformal dynamics

KW - Foliation

KW - Harmonic or stationary measure

UR - https://www.scopus.com/pages/publications/38849145084

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DO - 10.1007/s00039-007-0606-y

M3 - Article

AN - SCOPUS:38849145084

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EP - 1105

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

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ER -

Random conformal dynamical systems

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