三次hsamnon - heiles系统双哈密顿结构的直接构造

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2020-01-01 DOI:10.7546/jgsp-57-2020-99-109

Nicola Sottocornola

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引用次数: 1

摘要

近几十年来，可积哈密顿系统中分离变量的问题得到了广泛的研究。最近的一种方法是基于所谓的Kowalewski条件，用于表征控制矩阵\(M\)，其特征值给出所需的坐标。本文直接计算了三次h - heiles系统的第二相容哈密顿结构，并以此方法得到了作为递归算子\(N\)的特征值的分离变量。最后从\(N\)重新得到控制矩阵\(M\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Direct Construction of a Bi-Hamiltonian Structure for Cubic Hénon-Heiles Systems

The problem of separating variables in integrable Hamiltonian systems has been extensively studied in the last decades. A recent approach is based on the so called Kowalewski's Conditions used to characterized a Control Matrix \(M\) whose eigenvalues give the desired coordinates. In this paper we calculate directly a second compatible Hamiltonian structure for the cubic Hénon-Heiles systems and in this way we obtain the separation variables as the eigenvalues of a recursion operator \(N\). Finally we re-obtain the Control Matrix \(M\) from \(N\).

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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