Phase portraits of random planar homogeneous vector fields
Dynamical Systems
2021-03-10 v2 Classical Analysis and ODEs
Abstract
We study the phase portraits with positive probability of random planar homogeneous vector fields of degree n. In particular, for n=1,2,3, we give a complete solution of the problem and, moreover, either we give the exact value of each probability or we estimate it by using the Monte Carlo method. It is remarkable that all but two of these phase portraits are characterized by their index at the origin and by their number of invariant straight lines through it.
Keywords
Cite
@article{arxiv.1911.11441,
title = {Phase portraits of random planar homogeneous vector fields},
author = {Anna Cima and Armengol Gasull and Víctor Mañosa},
journal= {arXiv preprint arXiv:1911.11441},
year = {2021}
}
Comments
30 pages, 4 figures