Dynamic and normal forms of implicit differential equations
type: Item
instance of: scholarly article
title: Dynamic and normal forms of implicit differential equations
zbMATH Open document ID: 1312.34135
author: Julien Aurouet
publication date: 2015-01-16T00:00:00Z
review text: The author studies the local dynamics of implicit differential equations of the form \(F(x,y,dy)=0\) in a neighbourhood of a singular point. He uses relationships between implicit systems and Liouvillian vector fields. Symplectic classification of the latter implies the classification of implicit equations by contact transformations. The author uses results on normal forms of vector fields of Brjuno, Siegel and Stolovitch in the complex case and of Sternberg in the real one, adapted to Liouvillian vector fields and symplectic transformations. He gives the classification of implicit differential equations according to dynamical invariants and conditions for the existence of local solutions based on normal forms.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34M15
zbMATH DE Number: 6387327
zbMATH Keywords: normal forms
zbMATH Keywords: implicit differential equations
zbMATH Keywords: Liouvillian vector fields
zbMATH Keywords: symplectic normalisation
zbMATH Keywords: contact transformation
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: aif.2900
OpenAlex ID: W2315836752
cites work: Q3903276
cites work: Q5679142
cites work: Q3316228
cites work: Q3736577
cites work: A remark on Liouville vector fields and a theorem of Manouchehri
cites work: Singularites generiques des equations differentielles multiformes
cites work: Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point
cites work: Formes normales d'équations differéntielles implicites et de champs de Liouville
cites work: Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
cites work: Iteration of analytic functions
cites work: Local Contractions and a Theorem of Poincare
cites work: On the Structure of Local Homeomorphisms of Euclidean n-Space, II
cites work: Q5301221
cites work: Q4877993
cites work: Singularities of vector fields
cites work: Sur les equations différentielles multiformes et leurs intégrales singulières
cites work: Algèbres commutatives de champs de vecteurs isochores
DOI: 10.5802/AIF.2900
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 6387327