Display Abstract

Title Configurations of limit cycles in Li\'{e}nard equations

Name Bartomeu Coll
Country Spain
Email tomeu.coll@uib.cat
Co-Author(s) F. Dumortier, R. Prohens
Submit Time 2014-02-27 14:23:07
Session
Special Session 103: Periodic solutions for dynamical systems
Contents
We show that every finite configuration of disjoint simple closed curves in the plane is topologically realizable as the set of limit cycles of a polynomial Li\'{e}nard equation. The related vector field $X$ is Morse-Smale. Moreover it has the minimum number of singularities required for realizing the configuration in a Li\'{e}nard equation. We provide an explicit upper bound on the degree of $X$, which is lower than the results obtained before, obtained in the context of general polynomial vector fields.