Abstract:

In this seminar I will comment on the paper "Alien limit cycles in Liénard equations," by Coll, Dumortier and Prohens that will be published in the Journal of Differential Equations (2013). This paper presents a three dimensional family of Liénard equations of type (3,2) exhibiting the bifurcation of an alien limit cycle.

References:

M. Caubergh, Limit cycles near Vector Fields of Center Type, Limburgs Universitair Centrum, Diepenbeek, Belgium, Thesis, 2004.

M. Caubergh, F. Dumortier, R. Roussarie, Alien limit cycles near a Hamiltonian 2-saddle cycle, C.R. Math. Acad. Sci. Paris 340 (8) (2005) 587-592.

M. Caubergh, F. Dumortier, R. Roussarie, Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle, Communications on Pure Appl. Anal. 6 (2007) 1-21.

F. Dumortier, R. Roussarie, Abelian integrals and limit cycles, J. Differential Equations 227 (2006) 116-165.

S. Luca, F. Dumortier, M. Caubergh, R. Ruossarie, Detecting alien limit cycles near a Hamiltonian 2-saddle cycle, Discrete Contin. Dyn. Syst. 2 (4) (2009) 723-781.