Sur les rapprochements par conjugaison en dimension 1 et classe C^1

Abstract

We prove that the space of actions of Z^d by C^1 (orientation-preserving) diffeomorphisms of either the interval or the circle is connected by arcs. This is proved by showing that all such actions can be C^0 conjugated via a 1-parameter family into diffeomorphisms that converge to either the trivial action or an action by Euclidean rotations. Extensions for nilpotent group actions are provided.

Final version, to appear in Compositio Mathematica, in French

Cited by in corpus (2)

• Fixed points of nilpotent actions on ${\mathbb{S}}^2$
• Small $C^1$ actions of semidirect products on compact manifolds