Generic behavior of a piecewise smooth vector field with non-smooth switching surface

TL;DR

This paper investigates the local behavior and classification of singularities in two-dimensional piecewise smooth vector fields with algebraic switching surfaces, focusing on stability and bifurcations.

Contribution

It provides new classification results for structural stability and bifurcations in 2D piecewise smooth vector fields with algebraic switching sets.

Findings

Classification of typical singularities

Results on structural stability

Analysis of codimension one bifurcations

Abstract

This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise smooth vector fields when the switching set is an algebraic variety. The main focus is to obtain classification results concerning structural stability and generic codimension one bifurcations.