Éléments de distorsion de Diff 0 (M)  [ Distortion elements of Diff 0 (M) ]
Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 1, p. 35-46

We consider, on a compact manifold, the group of diffeomorphisms that are isotopic to the identity. We show that every recurrent element is a distortion element. To prove this, we generalize a method used by Avila in the case of the group of diffeomorphisms of the circle. The method also provides a new proof of a result by Calegari and Freedman: on a sphere, in the group of homeomorphisms that are isotopic to the identity, every element is distorted.

Dans cet article, on montre que, dans le groupe Diff 0 (M) des difféomorphismes isotopes à l’identité d’une variété compacte M, tout élément récurrent est de distorsion. Pour ce faire, on généralise une méthode de démonstration utilisée par Avila pour le cas de Diff 0 (𝕊 1 ). La méthode nous permet de retrouver un résultat de Calegari et Freedman selon lequel tout homéomorphisme de la sphère isotope à l’identité est un élément de distorsion.

DOI : https://doi.org/10.24033/bsmf.2642
Classification:  37C85
Keywords: diffeomorphism, dynamical systems, geometric group theory
@article{BSMF_2013__141_1_35_0,
     author = {Militon, Emmanuel},
     title = {\'El\'ements de distorsion de $\mathrm {Diff}\_{0}^{\infty }(M)$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {141},
     number = {1},
     year = {2013},
     pages = {35-46},
     doi = {10.24033/bsmf.2642},
     zbl = {1291.37039},
     language = {fr},
     url = {http://www.numdam.org/item/BSMF_2013__141_1_35_0}
}
Militon, Emmanuel. Éléments de distorsion de $\mathrm {Diff}_{0}^{\infty }(M)$. Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 1, pp. 35-46. doi : 10.24033/bsmf.2642. http://www.numdam.org/item/BSMF_2013__141_1_35_0/

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