Classical integrable systems and billiards related to generalized Jacobians

被引：31

作者：

Fedorov, Y ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Math & Mech, Moscow 119899, Russia

来源：

ACTA APPLICANDAE MATHEMATICAE | 1999年 / 55卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Jacobian varieties; theta-functions; integrable systems; billiards;

D O I：

10.1023/A:1006178224117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study some classical integrable systems of dynamics (the Euler top in space, the asymptotic geodesic motion on an ellipsoid) which are linearized on unramified coverings of generalized Jacobian varieties. We find explicit expressions for so called root functions living on such coverings which enable us to solve the problems in terms of generalized theta-functions. In addition, general and asymptotic solutions for ellipsoidal billiards and the billiard in an ellipsoidal layer are obtained.

引用

页码：251 / 301

页数：51

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