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 vecto…
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 investig…
math.DS2025
The hybrid matching of Hurwitz systems
Luis Fernando Mello, Paulo Santana
In this paper we study planar hybrid systems composed by two stable linear systems, defined by Hurwitz matrices, in addition with a jump that can be a piecewise linear, a polynomia…