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.

引用

页码：533 / 553

页数：21

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