Results 151 to 160 of about 154,581 (190)
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, 1992
Perhaps the easiest description of differential Galois theory is that it is about algebraic dependence relations between solutions of linear differential equations. To clarify this statement, let us consider three examples. First consider the differential equation $$z(1-z){y}''+(\frac{1}{2}-\frac{7}{6}z){y}'+\frac{11}{3600}y = 0$$ (1.1)
F. Beukers
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Perhaps the easiest description of differential Galois theory is that it is about algebraic dependence relations between solutions of linear differential equations. To clarify this statement, let us consider three examples. First consider the differential equation $$z(1-z){y}''+(\frac{1}{2}-\frac{7}{6}z){y}'+\frac{11}{3600}y = 0$$ (1.1)
F. Beukers
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Algebraic Groups and Differential Galois Theory
, 2011T. Crespo, Z. Hajto
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Surjectivities, octonions and differential Galois theory
Communications in Algebra, 2017ABSTRACTWe provide an explicit description of the torsors associated to the three groups related to the octonions—the exceptional Lie group G2 and the spin groups Spin7 and Spin8—and construct generic differential Galois extensions for those groups.
L. Juan, A. Ledet
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ON NONLINEAR DIFFERENTIAL GALOIS THEORY
Chinese Annals of Mathematics, 2002The author continues his paper [see Le groupoide de Galois d'un feuilletage, Monogr. Enseign. Math. 38, 465-501 (2001; Zbl 1033.32020)] discussing a new Galois theory of nonlinear differential equations. Let \(X\) denote a (smooth) complex analytic manifold, and let \(\Aut(X)\) be the space of germs of invertible maps \((X,a)\to (X,b)\), \(a,b\in X ...
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1999
The differential Galois theory for linear differential equations is the Picard- Vessiot Theory. In this theory there is a very nice concept of “integrability” i.e., solutions in closed form: an equation is integrable if the general solution is obtained by a combination of algebraic functions (over the coefficient field), exponentiation of quadratures ...
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The differential Galois theory for linear differential equations is the Picard- Vessiot Theory. In this theory there is a very nice concept of “integrability” i.e., solutions in closed form: an equation is integrable if the general solution is obtained by a combination of algebraic functions (over the coefficient field), exponentiation of quadratures ...
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On the Galois Theory of Differential Fields
American Journal of Mathematics, 19551. Summary. In a preceding paper [7] there was presented a Galois theory, for a certaini kind of differenitial field extension called strongly normal. The Galois group of a strongly normal extension is enidowed with a structure very much like that of a group variety, as studied by Weil [14].
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Galois Theory of Linear Differential Equations
2003Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability ...
Marius van der Put, Michael F. Singer
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Geometric and differential Galois theories
2013On March 29-April 2, 2010, a meeting was organized at the Luminy CIRM (France) on geometric and differential Galois theories, witnessing the close ties these theories have woven in recent years. The present volume collects the Proceedings of this meeting.
Couveignes, Jean-Marc +3 more
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Integrability of dynamical systems through differential Galois theory : a practical guide
, 2009J. Morales-Ruiz, J. Ramis
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