Specific properties of the ODE's flow in dimension two versus dimension three
Analysis of PDEs
2021-11-04 v1
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 , where is a constant vector in R 2. Furthermore, several extensions of the
Keywords
Cite
@article{arxiv.2111.02090,
title = {Specific properties of the ODE's flow in dimension two versus dimension three},
author = {Marc Briane and Loïc Hervé},
journal= {arXiv preprint arXiv:2111.02090},
year = {2021}
}