Local Modeling of Liouville Foliations by Billiards: Implementation of Edge Invariants

被引：9
|
作者：
Vedyushkina, V. V. [1 ]
机构：
[1] Lomonosov Moscow State Univ, Fac Mech & Math, Chair Differential Geometry & Applicat, Moscow 119991, Russia
来源：
MOSCOW UNIVERSITY MATHEMATICS BULLETIN | 2021年 / 76卷 / 02期
基金：
俄罗斯科学基金会;
关键词：
integrable Hamiltonian systems; billiard; Liouville foliation; bifurcation diagram; Fomenko-Zieschang invariant; topological invariants; INTEGRABLE SYSTEMS; BIFURCATIONS;
D O I：
10.3103/S0027132221020091
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The local case of A. Fomenko conjecture on the possibility of modeling Liouville foliations by integrable billiards is discussed. An extended version of its statements on numerical invariants on the edge of the Fomenko-Zieschang invariant of the Liouville foliation is proved. We show the realization of the Liouville foliation with some combinations of numerical mark values on a fixed edge by an appropriate class of integrable billiards.
引用
收藏
页码：60 / 64
页数：5
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