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Isochronous Attainable Manifolds for Piecewise Smooth Dynamical Systems

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Abstract

Considering the concept of attainable sets for differential inclusions, we introduce the isochronous manifolds relative to a piecewise smooth dynamical systems in \(\mathbb {R}^{2}\) and \(\mathbb {R}^{3}\), and study how analytical and topological properties of such manifolds are related to sliding motion and to partially nodal attractivity conditions on the discontinuity manifolds. We also investigate what happens to isochronous manifolds at tangential exit points, where attractivity conditions cease to hold. In particular, we find that isochronous curves in \(\mathbb {R}^{2}\), which are closed simple curves under attractivity regime, become open curves at such points.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125, Bari, Italy

    Fabio V. Difonzo

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  1. Fabio V. Difonzo
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Correspondence to Fabio V. Difonzo.

Additional information

This work has been supported by REFIN Project, grant number 812E4967. The author also author gratefully acknowledges 2019 MIUR/PRIN Project: Discontinuous dynamical systems: theory, numerics and applications coordinated by Nicola Guglielmi.

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Difonzo, F.V. Isochronous Attainable Manifolds for Piecewise Smooth Dynamical Systems. Qual. Theory Dyn. Syst. 21, 6 (2022). https://doi.org/10.1007/s12346-021-00536-z

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  • DOI: https://doi.org/10.1007/s12346-021-00536-z

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