Restricted version of the infinitesimal Hilbert 16th problem

Abstract : The paper deals with an abelian integral of a polynomial 1- form along a family of real ovals of a polynomial (hamiltonian) in two variables (the integral is considered as a function of value of the hamiltonian). We give an explicit upper bound of the number of its zeros (assuming the hamiltonian ultra-Morse of arbitrary degree and ranging in a compact subset in the space of ultra-Morse polynomials of a given degree, and that the form has a smaller degree). This bound depends on the choice of the compact set and is exponential in the fourth power of the degree.
Type de document :
Pré-publication, Document de travail
2006
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00078858
Contributeur : Alexey Glutsyuk <>
Soumis le : mercredi 7 juin 2006 - 17:11:41
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31
Document(s) archivé(s) le : lundi 5 avril 2010 - 22:28:11

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  • HAL Id : ensl-00078858, version 1

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Alexey Glutsyuk, Yuli Ilyashenko. Restricted version of the infinitesimal Hilbert 16th problem. 2006. 〈ensl-00078858〉

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