Liouville integrability: An effective Morales–Ramis–Simó theorem. (May 2016)

• Record Type: Journal Article
• Authors: Aparicio-Monforte, A.; Dreyfus, T.; Weil, J.-A.
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 537
• Page End: 560
• Publication Date: 2016-05
• Subjects: 37J30 -- 34A05 -- 68W30 -- 34M03 -- 34M15 -- 34M25 -- 17B45 -- 20G45 -- 32G81 -- 34M05 -- 37K10 -- 17B80 -- 70H06; Hamiltonian systems -- Ordinary differential equations -- Complete integrability -- Differential Galois theory -- Computer algebra -- Lie algebras; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.08.009
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is in reduced form with an abelian Lie algebra. Thus, we obtain an effective way to check the Morales–Ramis–Simó criterion for testing meromorphic Liouville integrability of Hamiltonian systems.