J. Pontigo-Herrera

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20172025

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math.DS2023

Infinitesimal and tangential 16-th Hilbert problem on zero-cycles

J. L. Bravo, P. Mardesic, D. Novikov +1

In this paper, given two polynomials $f$ and $g$ of one variable and a $0$ -cycle $C$ of $f$ , we consider the deformation $f + ε g$ . We define two functions: the displacement function…

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…