2013 Fiscal Year Final Research Report
Variational approach to the n-body problem
| Project/Area Number |
22740104
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Osaka University (2011-2013)
Kyoto University (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 多体問題 / 変分法 / 周期解 / 天体力学 / 力学系 / カオス / 分岐 / 対称性 |
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| Research Abstract |
I proved the existence of periodic solutions with regularizable collisions in the n-body problem. This includes the proof of the existence of Schubart orbit with arbitrary masses in the collinear three-body problem, Broucke orbit in the isosceles three-body problem and Sekiguchi orbit in the symmetric collinear four-body problem. I also proved the existence of super-eight solution by using the variational method.We investigated the bifurcation phenomena on periodic solutions in the isosceles three-body problem.
I proved the non-integrability of the collinear three-body problem by using the collision manifold theory.
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