# American Institute of Mathematical Sciences

April  2013, 6(4): 861-890. doi: 10.3934/dcdss.2013.6.861

## Chaos in forced impact systems

 1 Dipartimento di Ingegneria Industriale e Scienze Matematiche 2 Marche Polytecnic University, Via Brecce Bianche 1 3 60131 Ancona 4 Department of Mathematical Analysis and Numerical Mathematics 5 Comenius University 6 Mlynsk dolina, 842 48 Bratislava

Received  October 2011 Revised  February 2012 Published  December 2012

We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed impact systems whose unperturbed part has a piecewise continuous impact homoclinic solution that transversally enters the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has impact solutions that behave chaotically. Applications of this result to quasi periodic systems are also given.
Citation: Flaviano Battelli, Michal Fe?kan. Chaos in forced impact systems. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 861-890. doi: 10.3934/dcdss.2013.6.861
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