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Chaos Induced by Sliding Phenomena in Filippov Systems

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Abstract

In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit \(\Gamma \). More specifically we prove that the first return map, defined nearby \(\Gamma \), is topologically conjugate to a Bernoulli shift with infinite topological entropy. In particular, we see that for each \(m\in \mathbb {N}\) it has infinitely many periodic points with period m. We also study the perturbed system and obtain similar results.

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Acknowledgements

We thank to the referee for his/her comments and suggestions which helped us to improve greatly the presentation of this paper. The authors are very grateful to Marco A. Teixeira for reading the paper and making helpful comments and suggestions. D.D.N. was supported by FAPESP Grants 2015/02517-6 and 2016/11471-2. G.P. was supported by FAPESP Grants 2015/02731-8 and 2016/05384-0.

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  1. Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Baruque de Holanda, 651, Cidade Universitária Zeferino Vaz, Campinas, SP, 13083-859, Brazil

    Douglas D. Novaes, Gabriel Ponce & Régis Varão

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  1. Douglas D. Novaes
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  2. Gabriel Ponce
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  3. Régis Varão
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Correspondence to Régis Varão.

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Novaes, D.D., Ponce, G. & Varão, R. Chaos Induced by Sliding Phenomena in Filippov Systems. J Dyn Diff Equat 29, 1569–1583 (2017). https://doi.org/10.1007/s10884-017-9580-8

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  • DOI: https://doi.org/10.1007/s10884-017-9580-8

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