Abstract
In this work we discuss the appearance of minimal trajectories for the flow of piecewise smooth dynamical systems defined in the two dimensional torus and sphere in such a way that the switching manifold breaks the manifold into two connected components. We show that the number of pseudo-singularities of the sliding vector field is an invariant for the structural stability and study global bifurcations. Using a generic normal form, we prove that these systems can present chaotic behavior.
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Acknowledgements
R.M. Martins is supported by FAPESP-Brazil project 2015/06903-8. 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 CNPq-Brazil grants 478230/2013-3 and 443302/2014-6. This work was partially realized at UFG/Brazil as a part of project numbers 35796 and 040393 and also at CRM Barcelona, Spain. Part of this work was done during a visit of the first author to CRM Barcelona, Spain.
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Martins, R.M., Tonon, D.J. (2017). The Chaotic Behavior of Piecewise Smooth Dynamical Systems on Torus and Sphere. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_22
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DOI: https://doi.org/10.1007/978-3-319-55642-0_22
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