The monodromy problem and the tangential center problem |
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Authors: | C Christopher P Marde?i? |
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Institution: | 1.School of Mathematics and Statistics,London,UK;2.Institut de Mathematiques de Bourgogne, Unité Mixte de Recherche 5584 du C.N.R.S.,Universite de Bourgogne,Dijon,France |
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Abstract: | We consider families of Abelian integrals arising from perturbations of planar Hamiltonian systems. The tangential center-focus problem asks for conditions under which these integrals vanish identically. The problem is closely related to the monodromy problem, which asks when the monodromy of a vanishing cycle generates the whole homology of the level curves of the Hamiltonian.
We solve both of these questions for the case in which the Hamiltonian is hyperelliptic. As a by-product, we solve the corresponding
problems for the 0-dimensional Abelian integrals defined by Gavrilov and Movasati. |
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