Existence of a Center Manifold in a Practical Domain around L1 in the Restricted Three-Body Problem

被引：25

作者：

Capinski, Maciej J. ^{[1
]}

Roldan, Pablo ^{[2
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

[2] ETSEIB UPC, Dept Matemat Aplicada 1, Barcelona 08028, Spain

来源：

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2012年 / 11卷 / 01期

关键词：

center manifolds; normal forms; celestial mechanics; restricted three-body problem; covering relations; cone conditions; COVERING RELATIONS; SCATTERING MAP;

D O I：

10.1137/100810381

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a method of proving existence of center manifolds within specified domains. The method is based on a combination of topological tools, normal forms, and rigorous computer-assisted computations. We apply our method to obtain a proof of a center manifold in an explicit region around the equilibrium point L-1 in the Earth-Sun planar restricted circular three-body problem.

引用

页码：285 / 318

页数：34

共 50 条

[1] Structure of the centre manifold of the L1, L2 collinear libration points in the restricted three-body problem
Pucacco, Giuseppe
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2019, 131 (10):
[2] On the problem of convexity for the restricted three-body problem around the heavy primary
Frauenfelder, Urs
van Koert, Otto
Zhao, Lei
HOKKAIDO MATHEMATICAL JOURNAL, 2022, 51 (02) : 287 - 317
[3] Existence and Stability of L4,5 In The Relativistic Restricted Three-Body Problem
K. B. Bhatnagar
P. P. Hallan
Celestial Mechanics and Dynamical Astronomy, 1997, 69 : 271 - 281
[4] Existence and stability of L4,5 in the relativistic restricted three-body problem
Bhatnagar, KB
Hallan, PP
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 1997, 69 (03): : 271 - 281
[5] Frequencies and resonances around L4 in the elliptic restricted three-body problem
Rajnai, R.
Nagy, I.
Erdi, B.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2014, 443 (03) : 1988 - 1998
[6] Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification
Capinski, Maciej J.
Gidea, Marian
de la Llave, Rafael
NONLINEARITY, 2017, 30 (01) : 329 - 360
[7] From the restricted to the full three-body problem
Meyer, KR
Schmidt, DS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (05) : 2283 - 2299
[8] Halo orbits around the collinear points of the restricted three-body problem
Ceccaroni, Marta
Celletti, Alessandra
Pucacco, Giuseppe
PHYSICA D-NONLINEAR PHENOMENA, 2016, 317 : 28 - 42
[9] Dynamics in the center manifold of the collinear points of the restricted three body problem
Jorba, A
Masdemont, J
PHYSICA D, 1999, 132 (1-2): : 189 - 213
[10] Caustics of the restricted three-body problem
Santos, DE
Martins, RV
Winter, OC
Cordeiro, RR
ASTRONOMY & ASTROPHYSICS, 1998, 331 (03): : 1108 - 1112

← 1 2 3 4 5 →