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.

引用

页码：1645 / 1664

页数：20

共 50 条

[31] First-principle path integral study of DNA under hydrodynamic flows
Yang, SL
Witkoskie, JB
Cao, JS
CHEMICAL PHYSICS LETTERS, 2003, 377 (3-4) : 399 - 405
[32] On the Properties of Holomorphically 2-Geodesic Transformations of the First Linear Type of Almost Hermitian Structures
Suleimanova, E. A.
RUSSIAN MATHEMATICS, 2007, 51 (12) : 84 - 87
[33] On the properties of holomorphically 2-geodesic transformations of the first linear type of almost Hermitian structures
E. A. Suleimanova
Russian Mathematics, 2007, 51 (12) : 84 - 87
[34] Integral Representation of Linear Free-Surface Potential Flows for Bottom Pressure Calculation
Nguyen, T. C.
OCEANS 2009, VOLS 1-3, 2009, : 333 - 342
[35] On One Class of Nonclassical Linear Volterra Integral Equations of the First Kind
A. Asanov
T. Bekeshov
Ukrainian Mathematical Journal, 2020, 72 : 177 - 190
[36] On One Class of Nonclassical Linear Volterra Integral Equations of the First Kind
Asanov, A.
Bekeshov, T.
UKRAINIAN MATHEMATICAL JOURNAL, 2020, 72 (02) : 177 - 190
[37] Regularization and stability of systems of linear Fredholm integral equations of the first kind
Asanov, A.
Kadenova, Z. A.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2005, (38): : 11 - 14
[38] A class linear integral equations of Fredholm-Stilties of the first kind
Asanov, A.
Kalimbetov, B.
Toiygonbaeva, A.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2012, 68 (04): : 3 - 7
[39] A class of linear integral equations of the first kind with two independent variables
Imanaliev, M. I.
Asanov, A.
Kadenova, Z. A.
DOKLADY MATHEMATICS, 2014, 89 (01) : 98 - 102
[40] Regularization of Volterra Linear Integral Equations of the First Kind with the Smooth Data
Karakeev, T. T.
Imanaliev, T. M.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2020, 41 (01) : 39 - 45

← 1 2 3 4 5 →