J. Pontigo-Herrera

collaborators

3 papers

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…