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Sur la dynamique unidimensionnelle en r\'egularit\'e interm\'ediaire

Research paper by Bertrand Deroin, Victor Kleptsyn, Andres Navas

Indexed on: 08 Jan '06Published on: 08 Jan '06Published in: Mathematics - Dynamical Systems



Abstract

Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate some generalizations of Denjoy's Theorem and the classical Kopell's Lemma for Abelian groups. After that, these techniques are applied to the study of codimension 1 foliations. We obtain for instance several generalized versions of Sacksteder's Theorem in class $C^1$. We conclude with some remarks about the stationary measure.