The Successive Derivatives of the Period Function of a Plane Vector Field
作者： J.-P. Françoise
关键词: Cohomology 、 Hamiltonian (quantum mechanics) 、 Mathematical analysis 、 Bifurcation theory 、 Melnikov method 、 Return mapping 、 Computation 、 Vector field 、 Mathematics 、 Pure mathematics 、 Analysis
摘要: Previously, we provided an expression which generalized the classical Melnikov function to any order, for first nonzero derivative of a return mapping. Our method relied on decomposition 1-form associated relative cohomology perturbed Hamiltonian. With same techniques, give formula period function. We focus particular example ofH=(1/2)(x2+y2) and then define class Hamiltonians computation remains valid. Finally, investigate relations with Birkhoff normal form.
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