Abstract

Consider a family of planar systems depending on two parameters (n,b) and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when f(n,b)=0. We present a method that allows to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set f(n,b)=0. The method is applied to two quadratic families, one of them is the well-known Bogdanov-Takens system.

During the talk I'll explain the computational difficulties and how to solve them.

This is a joint work with A. Gasull and H. Giacomini.