Integrable Systems of Neumann Type

被引：3
|
作者：
Dobrogowska, Alina [1 ,2 ]
Ratiu, Tudor S. [1 ,3 ]
机构：
[1] Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland
[2] Univ Bialystok, Inst Math, PL-15424 Bialystok, Poland
[3] Ecole Polytech Fed Lausanne, Bernoulli Ctr, CH-1015 Lausanne, Switzerland
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2015年 / 27卷 / 3-4期
关键词：
Integrable system; Casimir function; Integrals in involution; Independence; Skew-symmetric matrices; Lie algebra deformation;
D O I：
10.1007/s10884-013-9314-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct families of integrable systems that interpolate between -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symmetric matrices and a certain deformation thereof. Involution is proved directly, since the standard involution theorems do not apply to these families. It is also shown that the integrals are independent.
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页码：533 / 553
页数：21
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