Chaos in forced impact systems (Q1942813)

The aim of this paper is to develop a Melnikov method for showing chaos in a time-perturbed impact system whose unperturbed part has a piecewise continuous impact homoclinic orbit entering the discontinuity manifold in a transversal way. A Melnikov function is defined in such a way that the existence of a simple zero means that the system has impact solutions that behave chaotically in the sense of Smale. The time influence can be periodic or almost periodic and the system is allowed to have arbitrary finite dimension. The main result is illustrated using two concrete examples.