Melnikov theory for discontinuous systems


Melnikov theory gives a method to detect the presence of chaotic patterns in non-autonomous dynamical systems, using exponential dichotomy. Our purpose is to extend such a theory to discontinuous systems, in order to study real phenomena, such as dry friction pendula. We look for conditions sufficeint to guarantee the persistence of homoclinic trajectories and the insurgence of chaotic patterns, when a system is subject to small non-autonomous perturbations. We focus in particular in the possible presence of phenomena which have no correspondence in the classical smooth case.


Dott. Matteo Franca email: