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ON THE NUMBER OF ZEROS OF MELNIKOV FUNCTIONS

By Sergey Benditkis and Dmitry Novikov

Abstract

Abstract. We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order k of the Melnikov function. The generic case k = 1 was considered by Binyamini, Novikov and Yakovenko ( [BNY10]). The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.173.3306
Provided by: CiteSeerX
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