On the chaotic behaviour of discontinuous systems (Q650173)

By using a functional analytic approach, the authors study the problem of chaotic behaviour in time-perturbed discontinuous systems in which the unperturbed part has a piecewise \(C^1\) homoclinic solution that crosses transversally the discontinuity manifold. They show that the existence of a simple zero of a certain Melnikov-like function guarantees the existence of a continuous, piecewise \(C^1\)-smooth solution of the perturbed system shadowed by the homoclinic orbit. As applications, piecewise linear three-dimensional discontinuous differential equations with quasiperiodic perturbations are presented.