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arXiv · 1702.00613

Generic Singularities of 3D Piecewise Smooth Dynamical Systems

Otávio M. L. Gomide·Marco A. Teixeira
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Abstract

The aim of this paper is to provide a discussion on current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is presented. The main purpose of this work is to describe the dynamical features of a fold-fold singularity in its most basic form and to give a complete and detailed proof of its local structural stability (or instability). In addition, classes of all topological types of a fold-fold singularity are intrinsically characterized. Such proof essentially follows firstly from some lines laid out by Colombo, García, Jeffrey, Teixeira and others and secondly offers a rigorous mathematical treatment under clear and crisp assumptions and solid arguments. One should to highlight that the geometric-topological methods employed lead us to the completely mathematical understanding of the dynamics around a T-singularity. This approach lends itself to applications in generic bifurcation theory. It is worth to say that such subject is still poorly understood in higher dimension.

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Otávio M. L. Gomide, Marco A. Teixeira. 2017-02-02. Generic Singularities of 3D Piecewise Smooth Dynamical Systems. https://doi.org/10.1007/978-3-319-94015-1_15

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