DIRECT CONSTRUCTION OF A BI-HAMILTONIAN STRUCTURE FOR CUBIC HENON-HEILES SYSTEMS

被引：1

作者：

Sottocornola, Nicola ^{[1
]}

机构：

[1] Zayed Univ, Dept Math & Stat, Abu Dhabi, U Arab Emirates

来源：

JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS | 2020年 / 57卷

关键词：

Integrable systems; separation of variables; integration in quadratures; EXPLICIT INTEGRATION;

D O I：

10.7546/jgsp-57-2020-99-109

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 Henon-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.

引用

页码：99 / 109

页数：11