The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
type: Item
instance of: scholarly article
title: The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
zbMATH Open document ID: 0816.30005
author: Dana Schlomiuk
author: Jean Écalle
publication date: 1994-11-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75043
review text: We investigate two important objects attached to (local, analytic, and above all resonant) vector fields or diffeomorphisms, namely the nilpotent part (a classical, almost self-explanatory notion, but with a hitherto poorly understood pattern of divergence) and the distinguished form (a spherical `resonant form'', chart-dependent, yet perfectly canonical). We find their analytical expression in terms of two universal sets of coefficients (the moulds \(\$^ \bullet\) and \(\$^ \bullet\)) and completely describe their divergence properties with the help of resurgence equations. We derive therefrom yet another means of calculating all the holomorphic invariants of ``local objects'' (fields or diffeos), and conclude by sketching a few algebraic consequences of our construction.
Mathematics Subject Classification ID: 30B99
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 32B99
Mathematics Subject Classification ID: 32G99
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 683175
zbMATH Keywords: singularities
zbMATH Keywords: normal forms
zbMATH Keywords: resurgent functions
MaRDI profile type: Publication
OpenAlex ID: W2322111688
cites work: Q4769296
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DOI: 10.5802/AIF.1379
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 683175