Sur la dynamique unidimensionnelle en régularité intermédiaire

Bertrand Deroin; Victor Kleptsyn; Andres Navas

hal-00463790, version 1

Sur la dynamique unidimensionnelle en régularité intermédiaire

Bertrand Deroin ¹, Victor Kleptsyn () ², Andres Navas () ³

Acta Mathematica 199, 2 (2007) 199-262

Abstract: Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class (i.e. between C 1 and C 2). In particular, we show some generalizations of Denjoy theorem and the classical Kopell lemma for abelian groups. These techniques are also applied to the study of codimension-1 foliations. For instance, we obtain several generalized versions of Sacksteder theorem in class C 1. We conclude with some remarks about the stationary measure.

1: Laboratoire de Mathématiques d'Orsay (LM-Orsay)
CNRS : UMR8628 – Université Paris XI - Paris Sud
2: Institut de Recherche Mathématique de Rennes (IRMAR)
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
3: University of Santiago, Chile
University of Santiago, Chile

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Submitted on: Monday, 15 March 2010 10:28:23
Updated on: Monday, 15 March 2010 10:28:23

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DOI: 10.1007/s11511-007-0020-1

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