Integrability of Hamiltonian systems and the Lamé equation

doi:10.1016/j.aml.2004.03.019

Applied Mathematics Letters

Volume 18, Issue 5, May 2005, Pages 555-561

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Abstract

We study the integrability of Hamiltonian systems with two degrees of freedom. We investigate the normal variational equations and obtain a necessary condition for integrability of these systems. As an application we study the integrability of the Hénon–Heiles system, whose normal variational equation is of Lamé type.

Keywords

Hamiltonian systems

NVE

Lamé equation

Basically periodic solutions

Monodromy matrix

Integrability

Hénon–Heiles system