Sur la dynamique unidimensionnelle en régularité intermédiaire

Details Sur la dynamique unidimensionnelle en régularité intermédiaire Sur la dynamique unidimensionnelle en régularité intermédiaire

2005-06-03

arxiv.org/abs/math/0506063v3

Acta Math. 199 no. 2 (2007) 199-262

Mathematics

Dynamical Systems

42 pages, 7 figures

Scientific paper

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.

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