Displaying similar documents to “A Galois D -groupoid for q -difference equations”

On a general difference Galois theory II

Shuji Morikawa, Hiroshi Umemura (2009)

Annales de l’institut Fourier

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We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.

Morales-Ramis Theorems Malgrange pseudogroup

Guy Casale (2009)

Annales de l’institut Fourier

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In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.

On a general difference Galois theory I

Shuji Morikawa (2009)

Annales de l’institut Fourier

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We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic 0 , we attach its Galois group, which is a group of coordinate transformation.

Canonical Objects in Classes of (n, V)-Groupoids

Celakoska-Jordanova, Vesna (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: 03C05, 08B20 Free algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras...