Variance of vector fields -- Definition and properties
Dynamical Systems
2026-01-12 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2601.05382,
title = {Variance of vector fields -- Definition and properties},
author = {Jacky Cresson and Jordy Palafox},
journal= {arXiv preprint arXiv:2601.05382},
year = {2026}
}