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 (Elsevier, 2020)
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.
Keywords: Bifurcation; Fold-fold singularity; Hamiltonian vector field; Limit cycle; Piecewise smooth vector field