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

2021/11/03 by Marc Briane, Briane, Marc, Loı̈c Hervé +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2111.02090

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 ζ, where ζ is a constant vector in R 2. Furthermore, several extensions of the

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