72 citations · 117 across the 35 of their papers we have counts for
12 papers · 1 filter
Infinitesimal and tangential 16-th Hilbert problem on zero-cycles
J. L. Bravo, P. Mardesic, D. Novikov +1
In this paper, given two polynomials and of one variable and a -cycle of , we consider the deformation . We define two functions: the displacement function…
Linear first order differential operators and their Hutchinson-invariant sets
Per Alexandersson, Nils Hemmingsson, Dmitry Novikov +2
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of…
Infinite Orbit depth and length of Melnikov functions
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
In this paper we study polynomial Hamiltonian systems in the plane and their small perturbations: . The first nonzero Melnikov function of the Poin…
Godbillon-Vey sequence and Francoise algorithm
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
We consider foliations given by deformations of exact forms in in a neighborhood of a family of cycles . In 1996 Francoise gave a…
Pseudo-Abelian integrals on slow-fast Darboux systems
Marcin Bobienski, Pavao Mardesic, Dmitry Novikov
We study pseudo-Abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number o…
On the number of zeros of Melnikov functions
Dmitry Novikov, Sergey Benditkis
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 vec…