J. Pontigo-Herrera

activity

20172025

collaborators

6 papers

math.CA2025

Noetherianity and length of Melnikov functions

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

We study foliations in $C^{2}$ given by polynomial deformations of the form $d H + ε η = 0$ , with $γ (t) \subset H^{- 1} (t)$ a family of cycles. The \emph{Poincaré first return map}…

math.CA2024

Nilpotence of Orbits under Monodromy and the Length of Melnikov Functions

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

Let $F \in C [x, y]$ be a polynomial, $γ (z) \in π_{1} (F^{- 1} (z))$ a non-trivial cycle in a generic fiber of $F$ and let $ω$ be a polynomial $1$ -form, thus defining a polynomial d…

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…

math.CA2017

Bounding the length of iterated integrals of the first nonzero Melnikov function

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

We consider small polynomial deformations of integrable systems of the form $d F = 0$ , $F \in C [x, y]$ and the first nonzero term $M_{μ}$ of the displacement function $Δ(t,ε)=\sum…