CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
CENTER ZA UPORABNO MATEMATIKO IN TEORETICNO FIZIKO
UNIVERZA V MARIBORU $\bullet$ UNIVERSITY OF MARIBOR
MLADINSKA 3 $\bullet$ SI-2000 MARIBOR $\bullet$ SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Kolokvij
Centra za uporabno matematiko in teoretično fiziko

Cyclicity of Nilpotent Centers

Professor Dr. Douglas Shafer
Mathematics Department, UNC Charlotte, North Carolina, USA

Abstract: We investigate the cyclicity of centers of planar polynomial systems of differential equations of the form x' = y + R(x,y), y' = S(x,y), where R and S have no constant or linear terms. When R and S are homogeneous of odd degree then it is known that centers are characterized by existence of a formal integral, which in turn is characterized by vanishing of certain polynomials in the coefficients of R and S that are analogous to the focus quantities that exist in the nondegenerate case. We show how to relate these focus quantities to the generalized Lyapunov quantities and exploit this connection to obtain bounds on the number of limit cycles that can bifurcate from the center in several cases.

Kolokvij bo v sredo 14. oktobra 2015 ob 15:15 uri v seminarski sobi CAMTP, Mladinska 3, drugo nadstropje levo. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --