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Combing the Hairy Ball Using a Vector Field Without Equilibria

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Abstract

The main goal of this paper is to present a piecewise smooth vector field tangent to S2 without equilibrium points. Moreover, we will show that this vector field contains a chaotic non-trivial minimal set.

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Acknowledgments

The first author was supported by grant #2017/00883-0, São Paulo Research Foundation (FAPESP). The second one was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

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Authors and Affiliations

  1. Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, Ribeirão Preto, SP, 14040-901, Brazil

    Tiago Carvalho

  2. Instituto de Biociências, Letras e Ciências Exatas (IBILCE), Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Rua Cristóvão Colombo, 2265, São José do Rio Preto, SP, 15054–000, Brazil

    Luiz Fernando Gonçalves

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  1. Tiago Carvalho
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  2. Luiz Fernando Gonçalves
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Correspondence to Luiz Fernando Gonçalves.

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Carvalho, T., Gonçalves, L.F. Combing the Hairy Ball Using a Vector Field Without Equilibria. J Dyn Control Syst 26, 233–242 (2020). https://doi.org/10.1007/s10883-019-09446-5

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  • DOI: https://doi.org/10.1007/s10883-019-09446-5

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