On the number of limit cycles of some vector fields with a nilpotent node
by
María Jesús Alvarez
Universitat de les Illes Balears
Coauthors: Armengol Gasull, Rafel Prohens

In this work we present two criteria that give an upper bound for the number of limit cycles of some families of planar analytic vector fields. These families are defined by the sum of two quasi-homogeneous vector fields, being the origin a nilpotent node. By writing the differential equation in (p, q)-generalized polar coordinates, we introduce two functions that control the maximum number of limit cycles. We prove that, depending on which of these functions does not change sign, the upper bound is either two or three.

Date received: May 26, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calh-95.