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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Dedicated to Professor Russell Allan Johnson on the occasion of his 60th birthday.
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Battelli, F., Fečkan, M. On the Chaotic Behaviour of Discontinuous Systems. J Dyn Diff Equat 23, 495–540 (2011). https://doi.org/10.1007/s10884-010-9197-7
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DOI: https://doi.org/10.1007/s10884-010-9197-7