On the Number of Limit Cycles Bifurcating from the Linear Center with an Algebraic Switching Curve

This paper studies the perturbations of system $${\dot{x}}=y$$ , $${\dot{y}}=-x$$ under arbitrary polynomial with switching curve $$y = x^m$$ where m is a positive integer. By analysing first order Melnikov function, we obtain lower bound and upper maximum number limit cycles bifurcating from period annulus if function not identically 0.