Random Conformal Dynamical Systems

By B. Deroin, V. Kleptsyn. 2005

71 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/53f1dba82579112b24a9e6f2f7fdae01ff4e032b

How researchers see this paper

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In Applied Mathematics

1. John Erik Fornæss
2. N. Sibony
3. Andrés Navas
4. T. Dinh
5. Tuyen T. T. Truong
6. Romain Dujardin
7. Nguyen-Bac Dang

In Geometry and Topology

1. John Erik Fornæss
2. N. Sibony
3. Andrés Navas
4. T. Dinh
5. Romain Dujardin
6. De-Qi Zhang
7. Tuyen T. T. Truong
8. Franccois Berteloot

In Mathematical Physics

1. N. Sibony
2. Andrés Navas
3. John Erik Fornæss
4. T. Dinh
5. Nguyen-Bac Dang
6. De-Qi Zhang
7. Franccois Berteloot
8. Tuyen T. T. Truong

Citations in the corpus

• Riemann Surface Laminations with Singularities (2008, background): “Remark 9 Recently, Deroin-Klepsyn [ 25 ] obtained a different proof of this result, assuming that X is minimal for a transversally conformal foliation.”
• GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, background): “(Uniqueness of the stationary measure in this setting and, more generally, in a transversely conformal framework, is the main content of [33].”