Dynamic and normal forms of implicit differential equations

DOI10.5802/aif.2900zbMath1312.34135OpenAlexW2315836752MaRDI QIDQ486828

Julien Aurouet

Publication date: 16 January 2015

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/aif.2900

zbMATH Keywords

normal formsimplicit differential equationscontact transformationLiouvillian vector fieldssymplectic normalisation

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Cites Work

• Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point
• Singularities of vector fields
• Iteration of analytic functions
• Local Contractions and a Theorem of Poincare
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• A remark on Liouville vector fields and a theorem of Manouchehri
• Algèbres commutatives de champs de vecteurs isochores
• Sur les equations différentielles multiformes et leurs intégrales singulières
• Singularites generiques des equations differentielles multiformes
• Formes normales d'équations differéntielles implicites et de champs de Liouville
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