3 papers
math.DS2026
Homoclinic Theorems for piecewise smooth vector fields
Claudio Buzzi, Paulo Santana, Luan V. M. F. Silva
In this paper we provide extensions of the Birkhoff-Smale Homoclinic Theorem and the -Lemma for piecewise smooth vector fields free of sliding motion. We prove that if the vect…
math.DS2025
A Piecewise Smooth -Lemma
Claudio A. Buzzi, Paulo Santana, Luan V. M. F. Silva
In this paper we provide extensions of the -Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investi…
math.DS2024
A Melnikov analysis on a family of second order discontinuous differential equations
Douglas D. Novaes, Luan V. M. F. Silva
This paper aims to provide a Melnikov-like function that governs the existence of periodic solutions bifurcating from period annuli in certain families of second-order discontinuou…