On the number of zeros of Melnikov functions
Dynamical Systems
2010-07-06 v1 Classical Analysis and ODEs
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 of the Melnikov function. The generic case was considered by Binyamini, Novikov and Yakovenko (\cite{BNY-Inf16}). The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals.
Keywords
Cite
@article{arxiv.1007.0672,
title = {On the number of zeros of Melnikov functions},
author = {Dmitry Novikov and Sergey Benditkis},
journal= {arXiv preprint arXiv:1007.0672},
year = {2010}
}