arXiv subjects

Jordy Palafox

Publications and source records attributed to Jordy Palafox.

4 recordsLinked to original sources

arXiv2026

Variance of vector fields -- Definition and properties

We give a self contained presentation of the notion of variance of a vector field introduced by Jean Ecalle and Bruno Vallet in \cite{ev} following a previous work of Jean Ecalle and Dana Schlomiuk in \cite{es}. We give complete proofs and definitions of various results stated in these articles. Following J. Ecalle and D. Schlomiuk, We illustrate the interest of the variance by giving a complete proof of the formulas for the mould defining the nilpotent part of a resonant vector field.

math.DS↗

arXiv2023

Application des groupes de Lie {à} la recherche des sym{é}tries des tissus implicites du plan

Alain H{é}naut's results on implicit web symmetry groups are revisited in the usual framework of Lie group actions on differential equations. A link is also given between the Lie algebra of fabric symmetries and the existence of Darboux polynomials.

math.DS↗

arXiv2017

Lie algebras and geometric complexity of an isochronous center condition

Using the mould formalism introduced by Jean Ecalle, we define and study the geometric complexity of an isochronous center condition. The role played by several Lie ideals is discussed coming from the interplay between the universal mould of the correction and the different Lie algebras generated by the comoulds. This strategy enters in the general program proposed by J. Ecalle and D. Schlomiuk in \cite{es} to study the size and splitting of some Lie ideals for the linearisability problem.

math.DS↗

arXiv2016

Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat

We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

math.DS↗