PERIODIC SOLUTIONS OF THE PLANAR N-CENTER PROBLEM WITH TOPOLOGICAL CONSTRAINTS

被引：17
|
作者：
Yu, Guowei [1 ]
机构：
[1] Univ Toronto, Dept Math, 40 St George St, Toronto, ON M5S 2E4, Canada
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 09期
基金：
加拿大自然科学与工程研究理事会;
关键词：
N-center problem; variational method; topological constraints; 3-BODY PROBLEM; PARABOLIC TRAJECTORIES; SYMBOLIC DYNAMICS; 4-BODY PROBLEM; EQUAL MASSES; BODY PROBLEM; EXISTENCE; ORBITS; SYSTEMS;
D O I：
10.3034/dcds.2016023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the planar N-center problem, given a non-trivial free homotopy class of the configuration space satisfying certain conditions, we show that there is at least one collision-free T-periodic solution for any positive T. The direct method of calculus of variations is used and the main difficulty is to show that minimizers under certain topological constraints are free of collision.
引用
收藏
页码：5131 / 5162
页数：32
相关论文
共 50 条
  • [11] Elementary solutions of the quantum planar two-center problem
    Gonzalez Leon, M. A.
    Mateos Guilarte, J.
    de la Torre Mayado, M.
    EPL, 2016, 114 (03)
  • [12] ACTION-MINIMIZING PERIODIC AND QUASI-PERIODIC SOLUTIONS IN THE n-BODY PROBLEM
    Chen, Kuo-Chang
    Ouyang, Tiancheng
    Xia, Zhihong
    MATHEMATICAL RESEARCH LETTERS, 2012, 19 (02) : 483 - 497
  • [13] Blow-Up, Homotopy and Existence for Periodic Solutions of the Planar Three-Body Problem
    Montgomery, Richard
    GEOMETRICAL THEMES INSPIRED BY THE N-BODY PROBLEM, 2018, 2204 : 49 - 89
  • [14] A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses
    Ouyang, Tiancheng
    Xie, Zhifu
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (07) : 4425 - 4455
  • [15] On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem
    Abouelmagd, Elbaz I.
    Alhowaity, Sawsan
    Diab, Zouhair
    Guirao, Juan L. G.
    Shehata, Mahmoud H.
    MATHEMATICS, 2022, 10 (04)
  • [16] Regularizable collinear periodic solutions in the n-body problem with arbitrary masses
    Yu, Guowei
    ADVANCES IN MATHEMATICS, 2024, 457
  • [17] New periodic solutions for planar N+2-body problems
    Deng Chunhua
    Shiqing Zhang
    JOURNAL OF GEOMETRY AND PHYSICS, 2011, 61 (12) : 2369 - 2377
  • [18] Periodic solutions for planar four-body problems
    Deng, Chunhua
    Zhang, Shiqing
    JOURNAL OF GEOMETRY AND PHYSICS, 2009, 59 (09) : 1210 - 1215
  • [19] Periodic solutions of the N-body problem with Lennard-Jones-type potentials
    Sbano, L.
    Southall, J.
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2010, 25 (01): : 53 - 73
  • [20] An Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem
    Hu, Xijun
    Yu, Guowei
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 361 (02) : 709 - 736
12345