Symmetries of vector fields: The diffeomorphism centralizer

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula>-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.