CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS

CENTER ZA UPORABNO MATEMATIKO IN TEORETICNO FIZIKO

UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR

MLADINSKA 3 SI-2000 MARIBOR SLOVENIA

Phone +(386) (2) 2355 350 and 2355 351 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**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** --

-- Direktor