Tempesta Piergiulio, Tondo Giorgio
Departamento de Física Teórica II, Facultad de Físicas, Universidad Complutense, 28040 Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 2):046602. doi: 10.1103/PhysRevE.85.046602. Epub 2012 Apr 3.
We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multiseparable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional ωN manifold guarantees the separation of variables. As an application, we construct such chains for the Hénon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.
我们证明，广义勒纳德链的概念自然地允许在双哈密顿几何的背景下构建多可分离和超可积系统的理论。我们证明，由定义在四维ωN流形上的哈密顿函数生成的广义勒纳德链的存在保证了变量的分离。作为应用，我们为亨农 - 海尔斯系统和经典的斯莫罗丁斯基 - 温特尼茨系统构造了这样的链。还发现了开普勒势的新双哈密顿结构。
