Liouville classification of integrable Hamiltonian systems on surfaces of revolution

被引：2
作者：
Kantonistova E.O. [1 ]
机构：
[1] Moscow State University, Leninskie Gory, Moscow
来源：
Moscow University Mathematics Bulletin | 2015年 / 70卷 / 5期
关键词：
Potential Versus; Hamiltonian System; Geodesic Flow; Integrable Hamiltonian System;
D O I：
10.3103/S002713221505006X
中图分类号：
学科分类号：
摘要：
An algorithm for calculation of Fomenko-Zieschang invariants for Hamiltonian systems on 2-dimensional surfaces of revolution is described in the case of the potential V (r) = cos r. One typical example of such system is considered. Classic examples of systems equivalent to this system in the sense of Liouville are obtained. It is shown that a system studied on a surface of revolution is Liouville equivalent to a geodesic flow on this surface. © 2015, Allerton Press, Inc.
引用
收藏
页码：220 / 222
页数：2
相关论文
共 11 条
  • [1] Bolsinov A.V., Fomenko A.T., Integrable Hamiltonian Systems. Geometry, Topology, Classification, (2004)
  • [2] Bolsinov A.V., Richter P., Fomenko A.T., The Method o f Loop Molecules and the Topology o f the Kovalevskaya Top, Matem. Sborn., 191, 2, (2000)
  • [3] Bolsinov A.V., Sbornik: Math., 191, 2, (2000)
  • [4] Trofimov V.V., Fomenko A.T., Liouville Integrability of Hamiltonian Sjstems on Lie Algebras, Uspeklii Matem. Nauk, 39, 2, (1984)
  • [5] Trofimov V.V., Russian Math. Surv., 39, 2, (1984)
  • [6] Brailov A.V., Fomenko A.T., The Topology o f Integral Submanifolds o f Completely Integrable Hamiltonian Sjstems, Matem. Sborn., 133, 3, (1987)
  • [7] Brailov A.V., Mathematics of the USSR Sbornik, 62, 2, (1989)
  • [8] Kantonistova E.O., Integer Lattices o f Action Angle Variables for “Spherical Pendulum” System, Vestn. Mosk. Univ., Matem. Meklian., 4, (2014)
  • [9] Kantonistova E.O., Moscow Univ. Math. Bull., 69, 4, (2014)
  • [10] Kantonistova E.O., Integer Lattices o f the Action Variables for the Generalized Lagrange Case, Vestn. Mosk. Univ., Matem. Meklian., 1, (2012)
12