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arXiv · 2111.02090

Specific properties of the ODE's flow in dimension two versus dimension three

Marc Briane·Loïc Hervé
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Abstract

This paper deals with the asymptotics of the ODE's flow induced by a regular vector field b on the d-dimensional torus R d /Z d. First, we start by revisiting the Franks-Misiurewicz theorem which claims that the Herman rotation set of any two-dimensional continuous flow is a closed line segment of R 2. Various general examples illustrate this result, among which a complete study of the Stepanoff flow associated with a vector field b = a $\zeta$, where $\zeta$ is a constant vector in R 2. Furthermore, several extensions of the

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Marc Briane, Loïc Hervé. 2021-11-03. Specific properties of the ODE's flow in dimension two versus dimension three. https://arxiv.org/abs/2111.02090

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