@inbook{5f4a9031bc0d4d7b8ef364026d3e366f,

title = "An inhomogeneous Picard-Fuchs equation",

abstract = "In the study of singularities of vector fields on the plane the analysis of perturbations of Hamiltonian systems is crucial. The number of isolated limit cycles in the perturbed system is related to the number of zeros of periods (Abelian integrals). If the Hamiltonian function is algebraic, then the there are finitely many independent periods. They satisfy a matrix linear homogeneous differential equation, the Picard-Fuchs equation. See for instance [BK81]. The average of the perturbed vector field over the periodic orbits of the unperturbed problem can be expressed in those periods.",

keywords = "Hamiltonian function, Abelian integral, Unperturbed problem, Monotonicity result, Homoclinic connection",

author = "{van Gils}, {Stephanus A.}",

year = "1994",

doi = "10.1007/978-94-011-0956-7_27",

language = "English",

isbn = "978-94-010-4413-4",

series = "NATO ASI Series C",

publisher = "Kluwer",

pages = "333--341",

editor = "Pascal Chossat",

booktitle = "Dynamics, Bifurcation and Symmetry",

address = "Netherlands",

note = "NATO Advanced Research Workshop on Dynamics, Bifurcation and Symmetry 1993 : New Trends and New Tools ; Conference date: 03-09-1993 Through 09-09-1993",

}