Prezada comunidade,

Nesta semana teremos a palestra do professor Joan Torregrosa (Universitat Autònoma de Barcelona, Espanha).

Título: Number of limit cycles for center families
Data: 20 de maio de 2026
Horário: 16h
Local: Auditório do DM

Resumo: Classical bifurcation mechanisms, such as degenerate Hopf bifurcation, Melnikov theory, and the averaging method, provide lower bounds for the number of limit cycles that a planar polynomial vector field of fixed degree can exhibit. Typically, the analysis focuses on a single center. In this talk, we show how exploiting families of centers can increase these lower bounds. In particular, we investigate how the cyclicity depends on the specific point within a connected component of centers. We present several examples, in both smooth and nonsmooth settings, illustrating this phenomenon under different perturbation techniques, near center points and heteroclinic connections.