On maximally superintegrable systems

被引：24
|
作者：
Tsiganov, A. V. [1 ]
机构：
[1] St Petersburg State Univ, VA Fock Inst Phys, St Petersburg 198504, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2008年 / 13卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
superintegrable systems; Toda lattices; Stackel systems;
D O I：
10.1134/S1560354708030040
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Locally any completely integrable system is maximally superintegrable system since we have the necessary number of the action-angle variables. The main problem is the construction of the single-valued additional integrals of motion on the whole phase space by using these multi-valued action-angle variables. Some constructions of the additional integrals of motion for the Stackel systems and for the integrable systems related with two different quadratic r-matrix algebras are discussed. Among these system there are the open Heisenberg magnet and the open Toda lattices associated with the different root systems.
引用
收藏
页码：178 / 190
页数：13
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