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Canonical Forms for Codimension One Planar Piecewise Smooth Vector Fields with Sliding Region

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Abstract

This paper is devoted to exhibit canonical forms for 2D codimension one piecewise smooth vector fields. All possible orientations and codimension one scenarios were covered. Also the intrinsic objects that characterize each one of the canonical forms were presented. As consequence, 62 canonical forms were obtained.

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Acknowledgements

The authors are gratefull to Professor John Hogan and professor Kristian Kristiansen for their suggestions, pointing some missing cases in [1]. T. Carvalho is partially supported by Grants #2017/00883-0 and #2013/34541-0, São Paulo Research Foundation (FAPESP), the CAPES/ Brazil Grants Nos. 88881.030454/ 2013-01 (from the Program CSF-PVE) and 1576689 (from the Program PNPD). T. Carvalho and D. J. Tonon are partially supported by the CNPq/Brazil Grants 478230/2013-3 and 443302/ 2014-6. D. J. Tonon is supported by Grant #2012/10 26 7000 803, Goiás Research Foundation (FAPEG), PROCAD/CAPES Grant 88881.0 68462/2014-01 and by CNPq-Brazil. This work is partially realized at UFG as a part of Project Nos. 35796, 35798 and 040393. J. L. Cardoso is partially supported by Goiás Research Foundation (FAPEG) and CAPES.

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Authors and Affiliations

  1. Departamento de Matemática, Faculdade de Ciências, UNESP, Av. Eng. Luiz Edmundo Carrijo Coube 14-01, Bauru, SP, CEP 17033-360, Brazil

    Tiago Carvalho

  2. Institute of Mathematics and Statistics of Federal University of Goiás, Avenida Esperança s/n, Campus Samambaia, Goiânia, GO, CEP 74690-900, Brazil

    João Lopes Cardoso & Durval José Tonon

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  1. Tiago Carvalho
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  2. João Lopes Cardoso
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  3. Durval José Tonon
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Correspondence to João Lopes Cardoso.

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Carvalho, T., Cardoso, J.L. & Tonon, D.J. Canonical Forms for Codimension One Planar Piecewise Smooth Vector Fields with Sliding Region. J Dyn Diff Equat 30, 1899–1920 (2018). https://doi.org/10.1007/s10884-017-9636-9

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  • DOI: https://doi.org/10.1007/s10884-017-9636-9

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