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On the Chaotic Behaviour of Discontinuous Systems

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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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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 1, 60131, Ancona, Italy

    Flaviano Battelli

  2. Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

Authors
  1. Flaviano Battelli
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  2. Michal Fečkan
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Correspondence to Flaviano Battelli.

Additional information

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

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