3 papers
math.DS2026
Planar constant piecewise smooth vector fields with large hysteresis
Tiago Carvalho, Leonardo Serantola, Bruno de Souza Rangel
Throughout this work, we will carry out a rigorous mathematical analysis of a class of control systems that is widely used in applications but still lacks a consistent theoretical…
math.DS2026
About the Shadowing Theorem for piecewise smooth vector fields with sliding motion
Tiago Carvalho
Since every modeling process in real-world situations is subject to errors, the study of the so-called shadowing property becomes highly relevant. This property allows for the iden…
math.DS2025
Canonical forms of 3d cusp-fold singularities and its unfoldings
Tiago Carvalho, Jackson Cunha, Bruno Rodrigues Freita
In this paper we obtain 32 canonical forms for 3D piecewise smooth vector fields presenting the so called cusp-fold singularity. All these canonical forms are topologically distinc…