The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
Dynamical Systems
2017-05-18 v2 Classical Analysis and ODEs
Abstract
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincar\'e--Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincar\'e--Liapunov method.
Keywords
Cite
@article{arxiv.math/0506116,
title = {The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems},
author = {Héctor Giacomini and Jaume Giné and Jaume Llibre},
journal= {arXiv preprint arXiv:math/0506116},
year = {2017}
}
Comments
24 pages, no figures