Explicit inhomogeneous Picard-Fuchs equations are obtained for Abelian integrals in piecewise smooth near-Hamiltonian systems, enabling recursive asymptotic expansions and bounds on the maximum number of isolated zeros of Melnikov functions near nilpotent saddle homoclinic loops.
Françoise, Successive derivatives of a first return map, application to the study of quadratic vector fields, Erg
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Inhomogeneous Picard-Fuchs equations of Abelian integrals in piecewise smooth near-Hamiltonian systems
Explicit inhomogeneous Picard-Fuchs equations are obtained for Abelian integrals in piecewise smooth near-Hamiltonian systems, enabling recursive asymptotic expansions and bounds on the maximum number of isolated zeros of Melnikov functions near nilpotent saddle homoclinic loops.