Variance of vector fields -- Definition and properties
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.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 January 2026
- Language
- EN
- Document type
- Preprint