On a galoisian approach to the splitting of separatrices
Juan J. Morales-Ruiz, Josep Maria Peris (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Displaying similar documents to “Integrability of hamiltonian systems and differential Galois groups of higher variational equations”
On a galoisian approach to the splitting of separatrices
Differential Galois approach to the non-integrability of the heavy top problem
Andrzej J. Maciejewski, Maria Przybylska (2005)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Galois theory of fuchsian q-difference equations
Jacques Sauloy (2003)
Annales scientifiques de l'École Normale Supérieure
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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.
Taylor obstruction to the integrability of homogeneous potentials of degree two. An application of higher order variational equations
Guillaume Duval, Andrzej J. Maciejewski (2011)
Banach Center Publications
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We show how using the differential Galois theory one can find effectively necessary conditions for the integrability of Hamiltonian systems with homogeneous potentials.
Recent work on differential Galois theory
Marius Van der Put (1997-1998)
Séminaire Bourbaki
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