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arXiv · 1708.07168

On the existence of limit cycles and invariant surfaces of sewing piecewise linear differential systems on $\mathbb{R}^3$

Bruno Rodrigues de Freitas·João Carlos Medrado
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Abstract

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique one-parameter family of periodic orbits, scrolls, invariant cylinders foliated by orbits which can be periodic or no.

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Bruno Rodrigues de Freitas, João Carlos Medrado. 2017-08-23. On the existence of limit cycles and invariant surfaces of sewing piecewise linear differential systems on $\mathbb{R}^3$. https://arxiv.org/abs/1708.07168

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