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On the Chaotic Behaviour of Discontinuous Systems |
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| Authors: | Flaviano Battelli Michal Fečkan |
| Institution: | 1. Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 1, 60131, Ancona, Italy 2. Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia 3. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, 814 73, Bratislava, Slovakia |
| Abstract: | We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C 1 homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given. |
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