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arXiv · 2601.05382

Variance of vector fields -- Definition and properties

Jacky Cresson·Jordy Palafox
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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.

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Jacky Cresson, Jordy Palafox. 2026-01-08. Variance of vector fields -- Definition and properties. https://arxiv.org/abs/2601.05382

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