An n Center Problem as an Example of a Geodesic Billiard Map with Singularities: Poincare Maps and Dynamics

被引：0

作者：

Garcia, Antonio ^{[1
]}

机构：

[1] Univ Autonoma Metropolitana Unidad Iztapalapa, Dept Matemat, Del Iztapalapa 09340, DF, Mexico

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2015年 / 14卷 / 02期

关键词：

Poincare maps; n-Center problem; Jacobi metric; Geodesic billiards; 2 FIXED CENTERS; OSCILLATORY SOLUTIONS; PLANAR;

D O I：

10.1007/s12346-015-0165-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the motion of a particle of infinitesimal mass and moving under the gravitational attraction of n particles of equal mass and fixed in the vertices of a regular polygon. The complete reduction of this problem is done using its finite group of symmetries. We show that it is the lift of a flow which is topologically conjugate to a geodesic billiard problem with the Jacobi metric and also study numerically the corresponding billiard maps.

引用

页码：209 / 225

页数：17

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