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Existence of periodic orbits for piecewise-smooth vector fields with sliding region via Conley theory

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 نشر من قبل Angie Tatiana Suarez Romero
 تاريخ النشر 2021
  مجال البحث
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The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined in a closed manifold of three dimensions without the scape region produces a semi-dynamical system. Thus, we have built a semiflow that allows us to apply the classical Conley theory. Furthermore, we use it to guarantee the existence of periodic orbits in this class of piecewise-smooth vector fields.



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