Abstract

We present the results of a joint work with D. Novikov, L. Ortiz-Bobadilla and J. Pontigo-Herrera.

In the work, we give a geometric bound for the length of the iterated integrals representing the first non-zero Melnikov functions of deformations of hamiltonian systems $dF+epsilonomega=0$. The bound depends only on the hamiltonian system $dF=0$ and not on the deformation $omega$.