On the number of limit cycles for polycycles $S^{(2)}$ and $S^{(3)}$ in quadratic Hamilton systems under perturbations of piecewise smooth polynomials

Jiaxin Wang, Liqin Zhao

In this paper, by using Picard-Fuchs equations and Chebyshev criterion, we study the bifurcate of limit cycles for quadratic Hamilton system $S^{(2)}$ and $S^{(3)}$: $\dot{x}= y+2a…