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Centralisateurs des difféomorphismes de la demi-droite

Hélène Eynard-Bontemps

Séminaire de théorie spectrale et géométrie

Soit $f$ un difféomorphisme lisse de $ℝ_{+}$ fixant seulement l’origine, et $𝒵^{r}$ son centralisateur dans le groupe des difféomorphismes $𝒞^{r}$ . Des résultat classiques de Kopell et Szekeres montrent que $𝒵^{1}$ est toujours un groupe à un paramètre. En revanche, Sergeraert a construit un $f$ dont le centralisateur $𝒵^{\infty}$ est réduit au groupe des itérés de $f$ . On présente ici le résultat principal de [] : $𝒵^{\infty}$ peut en fait être un sous-groupe propre et non-dénombrable (donc dense) de $𝒵^{1}$ .

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