English

Symmetries of vector fields: the diffeomorphism centralizer

Dynamical Systems 2019-03-15 v1

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 C1C^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.

Keywords

Cite

@article{arxiv.1903.05883,
  title  = {Symmetries of vector fields: the diffeomorphism centralizer},
  author = {Davi Obata},
  journal= {arXiv preprint arXiv:1903.05883},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-23T08:07:50.118Z