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arXiv · 2106.15569

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

Angie T. S. Romero·Ewerton R. Vieira
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Abstract

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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Angie T. S. Romero, Ewerton R. Vieira. 2021-07-27. Existence of periodic orbits for piecewise-smooth vector fields with sliding region via Conley theory. https://arxiv.org/abs/2106.15569

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