Morales-Ramis Theorems via Malgrange pseudogroup

Guy Casale[1]

  • [1] Université de Rennes 1 IRMAR-UMR 6625 CNRS 35042 Rennes Cedex (France)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 7, page 2593-2610
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Casale, Guy. "Morales-Ramis Theorems via Malgrange pseudogroup." Annales de l’institut Fourier 59.7 (2009): 2593-2610. <http://eudml.org/doc/10465>.

@article{Casale2009,
abstract = {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.},
affiliation = {Université de Rennes 1 IRMAR-UMR 6625 CNRS 35042 Rennes Cedex (France)},
author = {Casale, Guy},
journal = {Annales de l’institut Fourier},
keywords = {Differential Galois theory; variational equation; integrability; differential Galois theory},
language = {eng},
number = {7},
pages = {2593-2610},
publisher = {Association des Annales de l’institut Fourier},
title = {Morales-Ramis Theorems via Malgrange pseudogroup},
url = {http://eudml.org/doc/10465},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Casale, Guy
TI - Morales-Ramis Theorems via Malgrange pseudogroup
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 7
SP - 2593
EP - 2610
AB - 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.
LA - eng
KW - Differential Galois theory; variational equation; integrability; differential Galois theory
UR - http://eudml.org/doc/10465
ER -

References

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