Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

被引：29
|
作者：
Bahri, A [1 ]
Taimanov, IA
机构：
[1] Rutgers State Univ, Dept Math, New Brunswick, NJ 08903 USA
[2] Russian Acad Sci, Inst Math, Novosibirsk 630090, Russia
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 350卷 / 07期
关键词：
D O I：
10.1090/S0002-9947-98-02108-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Lagrangian system describing a motion of a charged particle on a Riemannian manifold is studied. For this flow an analog of a Ricci curvature is introduced, and for Ricci positively curved flows the existence of periodic orbits is proved.
引用
收藏
页码：2697 / 2717
页数：21
相关论文
共 50 条
  • [31] On the type of certain periodic orbits minimizing the Lagrangian action
    Arnaud, MC
    NONLINEARITY, 1998, 11 (01) : 143 - 150
  • [32] Periodic orbits in magnetic billiards
    L.G.G.V. Dias da Silva
    M.A.M. de Aguiar
    The European Physical Journal B - Condensed Matter and Complex Systems, 2000, 16 : 719 - 728
  • [33] Periodic orbits in magnetic billiards
    da Silva, LGGVD
    de Aguiar, MAM
    EUROPEAN PHYSICAL JOURNAL B, 2000, 16 (04): : 719 - 728
  • [34] Connecting orbits of autonomous Lagrangian systems
    Li, Xia
    Cheng, Chong-Qing
    NONLINEARITY, 2010, 23 (01) : 119 - 141
  • [35] Periodic orbits of oval billiards on surfaces of constant curvature
    dos Santos, Luciano Coutinho
    Pinto-de-Carvalho, Sonia
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2017, 32 (02): : 283 - 294
  • [36] On the periodic orbits of Hamiltonian systems
    Llibre, Jaume
    Rodrigues, Ana
    JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (04)
  • [37] Periodic orbits in gravitational systems
    Hadjedemetriou, John D.
    Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems, 2006, 227 : 43 - 79
  • [38] Using Lagrangian descriptors to calculate the Maslov index of periodic orbits
    Montes, J.
    Arranz, F. J.
    Borondo, F.
    PHYSICAL REVIEW E, 2024, 110 (01)
  • [39] THERMODYNAMICS OF SPIN SYSTEMS IN PERIODIC MAGNETIC-FIELDS
    FELDMAN, EB
    JETP LETTERS, 1984, 39 (12) : 657 - 659
  • [40] PERIODIC ORBITS IN PIECEWISE RICCATI VECTOR FIELDS
    Euzebio, Rodrigo D.
    Freitas, Bruno R.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (08): : 4325 - 4343
12345