Global Surfaces of Section in the Planar Restricted 3-Body Problem

被引：25

作者：

Albers, Peter ^{[1
]}

Fish, Joel W. ^{[2
]}

Frauenfelder, Urs ^{[4
]}

Hofer, Helmut ^{[3
]}

van Koert, Otto ^{[4
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] Inst Adv Study, Princeton, NJ 08540 USA

[4] Seoul Natl Univ, Inst Math, Dept Math & Res, Seoul, South Korea

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 204卷 / 01期

基金：

美国国家科学基金会;

关键词：

PERIODIC POINTS; CONVEX;

D O I：

10.1007/s00205-011-0475-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.

引用

页码：273 / 284

页数：12

共 22 条

[1]

ALBERS P., 2010, COMMUN PURE APPL MAT

[2]

Birkhoff GD, 1913, T AM MATH SOC, V14, P14

[3] Dynamical systems with two degrees of freedom [J].