On non-smooth vector fields having a torus or a sphere as the sliding manifold

2012/07/02 by Martins, Ricardo Miranda
#34A36 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.0397

Abstract

In this paper we consider a non-smooth vector field Z=(X,Y), where X,Y are linear vector fields in dimension 3 and the discontinuity manifold Σ of Z is or the usual embedded torus or the unitary sphere at origin. We suppose that Σ is a sliding (stable/unstable) manifold with tangencies, by considering X,Y inelastic over Σ. In each case, we study the tangencies of the vector field Z with Σ and describe the behavior of the trajectories of the sliding vector field over Σ: they are basically closed.

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