Realization of geodesic flows with a linear first integral by billiards with slipping

被引：2
|
作者：
Vedyushkina, V. V. [1 ]
Zav'yalov, V. N. [1 ]
机构：
[1] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia
来源：
SBORNIK MATHEMATICS | 2022年 / 213卷 / 12期
基金：
俄罗斯科学基金会;
关键词：
integrable system; billiard; geodesic flow; Liouville foliation; topological invariant; TOPOLOGICAL CLASSIFICATION; LIOUVILLE FOLIATIONS; SYSTEMS; IMPLEMENTATION; QUADRICS; GEOMETRY; METRICS;
D O I：
10.4213/sm9772e
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An arbitrary geodesic flow on the projective plane or Klein bottle with an additional, linear in the momentum, first integral is modelled using billiards with slipping on table complexes. The requisite table of a circular topological billiard with slipping is constructed algorithmically. Furthermore, linear integrals of geodesic flows can be reduced to the same canonical integral of a circular planar billiard. Bibliography: 36 titles.
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页码：1645 / 1664
页数：20
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