Invariant manifolds for piecewise smooth differential systems in ℝ³

2020/12/27 by Claudio A. Buzzi, Buzzi, Claudio A., Rodrigo D. Euzébio +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.2012.13951

arxiv created 2020/12/27 · arxiv updated 2020/12/29

Abstract

In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original differential system. These manifolds emerge from a continuum of cylinders of ℝ³ which does exist for the piecewise smooth differential systems after a rotation of some planar algebraic polynomial curves. The main tool used in order to obtain the results is the averaging theory for piecewise smooth differential systems.

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