6 papers
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…
Piecewise continuous and monotonic maps on the interval
Kleyber Cunha, Marcio Gouveia, Paulo Santana
Let be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this clas…
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…
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…
Phase portraits of (2;1) reversible vector fields of low codimension
C. Buzzi, J. Llibre, P. Santana
In this paper we study the phase portraits and bifurcation diagram of the symmetric singularities of codimensions zero, one and two of planar reversible vector fields having a line…
Limit cycles and chaos in planar hybrid systems
Jaume Llibre, Paulo Santana
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also…