Results 11 to 20 of about 154,581 (190)
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 ...
Elżbieta Adamus +3 more
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Generalized differential Galois theory [PDF]
Transactions of the American Mathematical Society, 2008 A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field extension.
Peter Landesman
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LARGE FIELDS IN DIFFERENTIAL GALOIS THEORY [PDF]
Journal of the Institute of Mathematics of Jussieu, 2017 We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over $\mathbb{Q}$ .
Annette Bachmayr +3 more
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Differential Galois theory of infinite dimension [PDF]
Nagoya Mathematical Journal, 1996 This paper is the second part of our work on differential Galois theory as we promised in [U3]. Differential Galois theory has a long history since Lie tried to apply the idea of Abel and Galois to differential equations in the 19th century (cf. [U3], Introduction). When we consider Galois theory of differential equation, we have to separate the finite
Hiroshi Umemura
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Differential Galois theory of linear difference equations [PDF]
Mathematische Annalen, 2008 We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
C. Hardouin, M. Singer
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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.
ANDRZEJ J. MACIEJEWSKI, MARIA PRZYBYLSKA
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Descent for differential Galois theory of difference equations. Confluence and q-dependency [PDF]
, 2011 The present paper contains two results that generalize and improve constructions of Hardouin and Singer. In the case of a derivation, we prove that the parametrized Galois theory for difference equations constructed by Hardouin and Singer can be ...
Lucia Di Vizio, Charlotte Hardouin
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Quantum integrable systems and differential Galois theory [PDF]
, 1996 This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry. We investigate the eigenvalue problem for such systems and the
Alexander Braverman +2 more
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Differential Galois Theory and Non-Integrability of Hamiltonian Systems [PDF]
, 1999 Juan José Morales Ruiz
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Differential Galois theory and non-integrability of planar polynomial vector fields [PDF]
Journal of Differential Equations, 2018 Primitivo B. Acosta-Humánez +3 more
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