Un point fixe commun pour des difféomorphismes commutants de $\mathrm{S}^2$

Abstract

Let $f_1,\ldots,f_n$ be $n$ commuting diffeomorphisms of the sphere $\mathrm{S}^2$, $C^1$-close to the identity; then they have a common fixed point. For the proof, we give a version of the Poincaré-Bendixson theorem, for the diffeomorphisms of $\mathrm{S}^2$, $C^1$-close to identity.