Differential Galois Theory and Lie-Vessiot Systems : Analytic and Algebraic Theory of Lie-vessiot Systems and Superposition Laws for Ordinary Differential Equations

Blazquez-sanz, David

ISBN 10: 3639096010 / ISBN 13: 9783639096019

Edité par VDM Verlag Dr. Mueller E.K., 2008

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Détails bibliographiques

• Titre: Differential Galois Theory and Lie-Vessiot Systems : Analytic and Algebraic Theory of Lie-vessiot Systems and Superposition Laws for Ordinary Differential Equations
• Éditeur: VDM Verlag Dr. Mueller E.K.
• Date de parution: 2008
• Langue: anglais
• ISBN à 10 chiffres: 3639096010
• ISBN à 13 chiffres: 9783639096019
• Reliure: Couverture souple
• État de l'article: As New

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Synopsis

The purpose of this work is to develop a differential Galois theory for differential equations admitting superposition laws. First, we characterize those differential equations in terms of Lie group actions, generalizing some classical results due to S. Lie. We call them Lie-Vessiot systems. Then, we develop a differential Galois theory for Lie-Vessiot systems both in the complex analytic and algebraic contexts. In the complex analytic context we give a theory that generalizes the tannakian approach to the classical Picard-Vessiot theory. In the algebraic case, we study differential equations under the formalism of differential algebra. We prove that algebraic Lie-Vessiot systems are solvable in strongly normal extensions. Therefore, Lie-Vessiot systems are differential equations attached to the Kolchin's differential Galois theory.