Details:
Title  A reduced form for linear differential systems and its application to integrability of Hamiltonian systems  Author(s)  Ainhoa AparicioMonforte, JacquesArthur Weil  Type  Article in Journal  Abstract  Let k be a differential field with algebraic closure k ̄ , and let [ A ] : Y ′ = A Y with A ∈ M n ( k ) be a linear differential system. Denote by g the Lie algebra of the differential Galois group of [ A ] . We say that a matrix R ∈ M n ( k ¯ ) is a reduced form of [ A ] if R ∈ g ( k ¯ ) and there exists P ∈ G L n ( k ¯ ) such that R = P − 1 ( A P − P ′ ) ∈ g ( k ¯ ) . Such a form is often the sparsest possible attainable through gauge transformations without introducing new transcendents. In this paper, we discuss how to compute reduced forms of some symplectic differential systems, arising as variational equations of Hamiltonian systems. We use this to give an effective form of the Morales–Ramis theorem on (non)integrability of Hamiltonian systems.  Keywords  Differential Galois theory, Computer algebra, Hamiltonian Systems, Integrability, Morales–Ramis theory, Reduced form  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111001465 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  2  Pages  192  213  Year  2012  Edition  0  Translation 
No  Refereed 
No 
