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.

中文翻译：

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矢量场的对称性：微分同胚中心化器

在本文中，我们研究了向量场的微分同胚中心化器：给定一个向量场，它是与流交换的微分同胚集合。我们的主要定理指出，对于至多具有有限多个汇点或源的 $C^1 $-泛型微分同胚，微分同胚中心化器是准平凡的。在某些情况下，我们可以将准平凡提升为平凡。我们还获得了一个标准，将集中器中的微分同胚作为流的重新参数化。