Separatrices for real analytic vector fields in the plane
Dynamical Systems
2019-12-02 v1 Classical Analysis and ODEs
Complex Variables
Abstract
Let be a germ of real analytic vector field at with an algebracally isolated singularity. We say that is a topological generalized curve if there are no topological saddle-nodes in its reduction of singularities. In this case, we prove that if either the order or the Milnor number is even, then has a formal separatrix, that is, a formal invariant curve at . This result is optimal, in the sense that these hypotheses do not assure the existence of a convergent separatrix.
Cite
@article{arxiv.1911.12803,
title = {Separatrices for real analytic vector fields in the plane},
author = {Eduardo Cabrera and Rogério Mol},
journal= {arXiv preprint arXiv:1911.12803},
year = {2019}
}
Comments
16 pages