# Configurations of limit cycles in Liénard equations

Date:
17.03.14
Times:
15:30 to 16:30
Place:
CRM - Auditori (C1/034)
Speaker:
Rafel Prohens
University:
Universitat de Les Illes Balears

#### Abstract:

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 Liénard equation. The related vector field $X$ is Morse-Smale. Moreover it has the minimum number of singularities required for realizing the configuration in a Liénard 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.