J. Pontigo-Herrera

activity

20172025

collaborators

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3 papers · 1 filter

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.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…