Results 11 to 20 of about 16,779 (193)
Differential Galois Theory and Integration [PDF]
, 2021 In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several examples to reduce the differential system.
Thomas Dreyfus, Jacques-Arthur Weil
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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.
David Blázquez-Sanz +2 more
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LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY [PDF]
Journal of the Institute of Mathematics of Jussieu, 2020 AbstractWe solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over $\mathbb{Q}$. More generally, we show that over such a field, every split differential embedding problem can be solved.
Annette Bachmayr +7 more
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Generalized differential Galois theory [PDF]
Transactions of the American Mathematical Society, 2008 71 pages, part of author's Phd ...
Peter Landesman
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On the geometrization of a lemma of differential Galois theory [PDF]
, 2010 42 pages ...
Colas Bardavid
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On the Constructive Inverse Problem in Differential Galois Theory [PDF]
Communications in Algebra, 2004 Several misprints have been corrected and the statement of Propositions 3.2 and 3.4 have been made more precise and their proofs ...
William J. Cook +2 more
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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 ...
Elżbieta Adamus +2 more
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Differential Galois theory I [PDF]
Annals of Pure and Applied Logic, 1998 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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An Extension of Differential Galois Theory [PDF]
Transactions of the American Mathematical Society, 1965 H. F. Kreimer
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Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
Symmetry, Integrability and Geometry: Methods and Applications, 2021 Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and applied in many frameworks, for instance in quantum mechanics (where they provide useful tools for supersymmetric ...
Primitivo B. Acosta-Humánez +3 more
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