Results 11 to 20 of about 16,850 (158)
Annals of Pure and Applied Logic, 1997 This paper proposes a generalization of Kolchin's Galois theory of differential fields. In the Kolchin theory, the Galois groups correspond to algebraic groups over the subfield of constants; moreover every algebraic group can arise in this way. In this paper, the constants are replaced by an arbitrary differential algebraic set \(X\). Accordingly, \(X\
Anand Pillay
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Meromorphic Non-Integrability of Several 3D Dynamical Systems
Entropy, 2017 In this paper, we apply the differential Galoisian approach to investigate the meromorphic non-integrability of a class of 3D equations in mathematical physics, including Nosé–Hoover equations, the Lü system, the Rikitake-like system and Rucklidge ...
Kaiyin Huang, Shaoyun Shi, Wenlei Li
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Generalized differential Galois theory [PDF]
Transactions of the American Mathematical Society, 2008 71 pages, part of author's Phd ...
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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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Triviality of differential Galois cohomology of linear differential algebraic groups. [PDF]
Commun Algebra, 2019 Minchenko A, Ovchinnikov A.
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Jacobian Conjecture via Differential Galois Theory [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partial differential fields, the theory of strongly normal extensions as presented by Kovacic and the ...
Adamus, Elżbieta +2 more
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Differential Galois Theory and Lie Symmetries [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems.
Blázquez-Sanz, David +2 more
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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.
Jiménez, S. +3 more
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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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