Results 21 to 30 of about 16,779 (193)
General differential Galois theory [PDF]
Moscow University Mathematics Bulletin, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dmitry Trushin
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DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY [PDF]
International Journal of Geometric Methods in Modern Physics, 2009 This paper is an overview of our works that are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of integrability obstructions for these systems are presented.
Maciejewski, Andrzej J. +1 more
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On the Inverse Problem in Differential Galois Theory
, 2002 Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the base field and commute with the derivation. Differential
Julia Hartmann
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Differential Galois Theory and Isomonodromic Deformations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois group of a connection with parameters with simple structural group $G$ is determined by its isomonodromic ...
Blázquez-Sanz, David +2 more
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ScienceOpen Research, 2016 By theorizing the physical reality through the deformation of an arbitrary cross-ratio, we leverage Galois differential theory to describe the dynamics of isomonodromic integratable system.
Jackie Liu
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Différentielles non commutatives et théorie de Galois différentielle ou aux différences [PDF]
, 2001 65 pagesWe show how the Galois-Picard_Vessiot theory of differential equations and difference equations, and the theory of holonomy groups in differential geometry, are different aspects of a unique Galois theory.
André, Yves
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Some definable Galois theory and examples [PDF]
, 2016 We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the constants are ...
Pillay, Anand, Sanchez, Omar Leon
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Galois theory, functional Lindemann-Weierstrass, and Manin maps [PDF]
, 2015 We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations.
Bertrand, Daniel, Pillay, Anand
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Rational KdV Potentials and Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 In this work, using differential Galois theory, we study the spectral problem of the one-dimensional Schr dinger equation for rational time dependent KdV potentials. In particular, we compute the fundamental matrices of the linear systems associated to the Schr dinger equation.
Jim Énez, Sonia +3 more
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Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions [PDF]
, 2019 We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular cases of interest, such as shift difference equations, q-dilation ...
Arreche, Carlos E. +2 more
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