Resumen de On the Number of Limit Cycles Bifurcating from the Linear Center with a Cubic Switching Curve

Ranran Jia, Liqin Zhao

• This paper studies the bifurcations of limit cycles from the system x˙ = y, y˙ = −x with the switching curve y = x3/3 − x under the perturbations of arbitrary polynomials of x and y with degree n. We obtain the lower bound and upper bound of the maximum number of limit cycles bifurcating from h ∈ (0, 3/2) if the first order Melnikov function is not identically 0. When the degree of perturbing terms is low, we obtain a precise result on the number of zeros of the first order Melnikov function. We also give an example to illustrate our result.