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arXiv · 1903.07065

A criterion for the triviality of the centralizer for vector fields and applications

Wescley Bonomo·Paulo Varandas
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Abstract

In this paper we establish a criterion for the triviality of the $C^1$-centralizer for vector fields and flows. In particular we deduce the triviality of the centralizer at homoclinic classes of $C^r$ vector fields ($r\ge 1$). Furthermore, we show that the set of flows whose $C^1$-centralizer is trivial include: (i) $C^1$-generic volume preserving flows, (ii) $C^2$-generic Hamiltonian flows on a generic and full Lebesgue measure set of energy levels, and (iii) $C^1$-open set of non-hyperbolic vector fields (that admit a Lorenz attractor). We also provide a criterion for the triviality of the $C^0$-centralizer of continuous flows.

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Wescley Bonomo, Paulo Varandas. 2019-03-17. A criterion for the triviality of the centralizer for vector fields and applications. https://doi.org/10.1016/j.jde.2019.02.022

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