Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems

de Carvalho Braga, Denis; Fernandes da Fonseca, Alexander; Gonçalves, Luiz Fernando [UNESP]; Mello, Luis Fernando

Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems

Data

2020-04-01

Autores

de Carvalho Braga, Denis

Fernandes da Fonseca, Alexander

Gonçalves, Luiz Fernando

Mello, Luis Fernando

Tipo

Artigo

Resumo

We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov coefficients. As a consequence, the bifurcation diagrams, illustrating the number, types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields, are determined.