Symmetries of vector fields: the diffeomorphism centralizer

Abstract

In this paper we study the diffeomorphism centralizer of a vector field: given a vector field it is the set of diffeomorphisms that commutes with the flow. Our main theorem states that for a $C^1$-generic diffeomorphism having at most finitely many sinks or sources, the diffeomorphism centralizer is quasi-trivial. In certain cases, we can promote the quasi-triviality to triviality. We also obtain a criterion for a diffeomorphism in the centralizer to be a reparametrization of the flow.

15 pages

References in corpus (2)

• Trivial centralizers for Axiom A diffeomorphisms
• A criterion for the triviality of the centralizer for vector fields and applications