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Více informací o knize Differential Galois Theory and Lie-Vessiot Systems

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• Anotace
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Anotace knihy

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. 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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics

• Plný název: Differential Galois Theory and Lie-Vessiot Systems
• Podnázev: Analytic and Algebraic Theory of Lie-Vessiot Systemsand Superposition Laws for Ordinary DifferentialEquations
• Autor: David Blázquez-Sanz
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 192
• EAN: 9783639096019
• ISBN: 3639096010
• ID: 06818648
• Nakladatelství: VDM Verlag Dr. Mueller E.K.
• Hmotnost: 263 g
• Rozměry: 229 × 152 × 10 mm
• Datum vydání: 29. October 2008

Oblíbené z jiného soudku

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