Des points fixes communs pour des difféomorphismes de S~2 qui commutent et préservent une mesure de probabilité some common fixed points for commuting conservative diffeomorphisms of the two-sphere

摘要

We prove the existence of common ?xed points for some homeomorphisms of the plane R~2 or the two-sphere S~2 which commute and preserve a probability measure. For example, if f1,...,fn are commuting C ~1-di?eomorphisms of S2 that are su?ciently close to the identity, and that preserve a probability measure whose support is not a single point, then they have at least two common ?xed points.