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.DS2025
On the cyclicity of hyperbolic polycycles
Claudio Buzzi, Armengol Gasull, Paulo Santana
Let be a planar smooth vector field with a polycycle with sides and all its corners, that are at most singularities, being hyperbolic saddles. In this paper we s…