Bookcover of Differential Galois Theory and Lie-Vessiot Systems
Booktitle:

Differential Galois Theory and Lie-Vessiot Systems

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

VDM Verlag Dr. Müller (2008-10-29 )

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ISBN-13:

978-3-639-09601-9

ISBN-10:
3639096010
EAN:
9783639096019
Book language:
English
Blurb/Shorttext:
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.
Publishing house:
VDM Verlag Dr. Müller
Website:
http://www.vdm-verlag.de
By (author) :
Blázquez-Sanz David
Number of pages:
192
Published on:
2008-10-29
Stock:
Available
Category:
Mathematics
Price:
68.00 €
Keywords:
Ordinary Differential Equations, Differential Galois Theory, Algebraic Groups, Integrability, Solvability, Superposition Laws, Strongly Normal Extensions.

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