D. Novikov

activity

20002026

most citedOn the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem

72 citations · 117 across the 35 of their papers we have counts for

collaborators

Showing 2019 · math.DSShow all

2 papers · 2 filters

math.DS2019

Infinite Orbit depth and length of Melnikov functions

Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1

In this paper we study polynomial Hamiltonian systems $d F = 0$ in the plane and their small perturbations: $d F + ε ω = 0$ . The first nonzero Melnikov function $M_{μ} = M_{μ} (F, γ, ω)$ of the Poin…

math.DS2019

Godbillon-Vey sequence and Francoise algorithm

Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1

We consider foliations given by deformations $d F + ε ω$ of exact forms $d F$ in $C^{2}$ in a neighborhood of a family of cycles $γ (t) \subset F^{- 1} (t)$ . In 1996 Francoise gave a…