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

[21] Motion in the generalized restricted three-body problem [J].

Singh, Jagadish ;

Taura, Joel John .

ASTROPHYSICS AND SPACE SCIENCE, 2013, 343 (01) :95-106

[22] The vanishing twist in the restricted three-body problem [J].

Dullin, Holger R. ;

Worthington, Joachim .

PHYSICA D-NONLINEAR PHENOMENA, 2014, 276 :12-20

[23] A Note on Modified Restricted Three-Body Problem [J].

Kumar, Dinesh ;

Sharma, Ram Krishan ;

Aggarwal, Rajiv ;

Chauhan, Shipra ;

Sharma, Arpana .

ASTRONOMY REPORTS, 2022, 66 (08) :710-724

[24] NEW REGULARIZATION OF THE RESTRICTED THREE-BODY PROBLEM [J].

Szucs-Csillik, Iharka ;

Roman, Rodica .

ROMANIAN ASTRONOMICAL JOURNAL, 2012, 22 (02) :135-144

[25] Capture conditions in the restricted three-body problem [J].

Brunini, A ;

Giordano, CM ;

Orellana, RB .

ASTRONOMY & ASTROPHYSICS, 1996, 314 (03) :977-982

[26] Motion in the generalized restricted three-body problem [J].

Jagadish Singh ;

Joel John Taura .

Astrophysics and Space Science, 2013, 343 :95-106

[27] A Note on Modified Restricted Three-Body Problem [J].

Dinesh Kumar ;

Ram Krishan Sharma ;

Rajiv Aggarwal ;

Shipra Chauhan ;

Arpana Sharma .

Astronomy Reports, 2022, 66 :710-724

[28] The restricted three-body problem with logarithm potential [J].

Muscas, A. -m. ;

Pasca, D. ;

Stoica, C. .

NEW ASTRONOMY, 2024, 105

[29] Classifying orbits in the restricted three-body problem [J].

Zotos, Euaggelos E. .

NONLINEAR DYNAMICS, 2015, 82 (03) :1233-1250

[30] Classifying orbits in the restricted three-body problem [J].

Euaggelos E. Zotos .

Nonlinear Dynamics, 2015, 82 :1233-1250

← 1 2 3 4 5 →