CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS

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

Anhui Normal University, Wuhu 241002, P.R. China

**Abstract:**
We consider a planar piecewise Hamiltonian system with a straight line of separation, which has a piecewise generalized homoclinic loop passing through a saddle-fold point and assume that there exists a family of piecewise smooth periodic orbits near the loop.
By studying the asymptotic expansion of the first order Melnikov
function corresponding to the period annulus we obtain the formulas of the first six coefficients in the expansion, based on which we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications two concrete systems are considered, where the first one reveals that a quadratic piecewise Hamiltonian system can have five limit cycles near a generalized homoclinic loop under a quadratic piecewise smooth perturbation. Compared with the smooth case, three more limit cycles are found.

**Seminarsko predavanje bo v sredo 15. marca 2017 ob 16:00 uri
v seminarski sobi CAMTP, Mladinska 3, drugo nadstropje levo.
Vljudno vabljeni vsi zainteresirani, tudi
študentje.**

Prof.Dr. Marko Robnik

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