Liouville integrability: An effective Morales-Ramis-Simó theorem

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• 作者：A. Aparicio-Monforte^a ; ^{aamonforte@dawsoncollege.qc.ca" class="auth_mail" title="E-mail the corresponding author} ; T. Dreyfus^b ; ^{tdreyfus@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author} ; J.-A. Weil^c ; ^{weil@unilim.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37J30 ; 34A05 ; 68W30 ; 34M03 ; 34M15 ; 34M25 ; 17B45 ; 20G45 ; 32G81 ; 34M05 ; 37K10 ; 17B80 ; 70H06
• 刊名：Journal of Symbolic Computation
• 出版年：2016
• 出版时间：May-June 2016
• 年：2016
• 卷：74
• 期：Complete
• 页码：537-560
• 全文大小：561 K

文摘

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.