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Computer Assisted Existence Proofs of Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun PCR3BP
被引：28
|作者：
Capinski, Maciej J.
[1
]
机构：
[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
来源：
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
|
2012年
/
11卷
/
04期
关键词：
invariant manifolds;
restricted three body problem;
cone conditions;
parameterization method;
computer assisted proofs;
CIRCULAR 3-BODY PROBLEM;
PERIODIC-ORBITS;
HETEROCLINIC CONNECTIONS;
COVERING RELATIONS;
CONE CONDITIONS;
STABILITY;
D O I：
10.1137/110847366
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L-2 (the collinear libration point between the primaries) up to half the distance to the smaller primary in the Jupiter-Sun planar circular restricted three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invariant manifolds intersect transversally. Our computer assisted proof provides explicit bounds on the location and on the angle of intersection.
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页码：1723 / 1753
页数：31
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