Resumen de A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System

Xiaoyan Chen, Maoan Han

• In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n. This result confirms a conjecture.