On the existence of limit cycles and invariant surfaces of sewing piecewise linear differential systems on ℝ³

2017/08/23 by Bruno Rodrigues de Freitas, de Freitas, Bruno Rodrigues, João C. Medrado +1
Mathematics · Computer Science · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical Control Systems and Analysis #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1708.07168

Abstract

We consider a class of discontinuous piecewise linear differential systems in ℝ³ 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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