Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications (Q2074451)

The authors investigate limit cycles bifurcating from periodic submanifold of \(n\)-dimensonal piecewise smooth dynamical systems with two zones separated by a hyperplane. In order to obtain the maximum number of limit cycles, they obtain arbitrary order Melnikov function by using Faá di Bruno's Formula. As applications, they study the maximum number of crossing limit cycles bifurcating from an \(n\)-dimensional periodic submanifold caused by non-smooth centers of fold-fold type and perturbations of piecewise smooth Hamiltonian systems. Moreover, they prove that these upper bounds can be reached. Their main results extend some known results in these directions.