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arXiv · 1903.05883

Symmetries of vector fields: the diffeomorphism centralizer

Davi Obata
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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.

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Davi Obata. 2019-03-14. Symmetries of vector fields: the diffeomorphism centralizer. https://arxiv.org/abs/1903.05883

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