| Project/Area Number |
26870289
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
Geometry
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| Research Institution | Ritsumeikan University (2016-2017)
Kyoto University (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Hamilton力学系 / 完全積分可能系 / Lie群 / 剛体 / 平衡点 / 安定性 / ファイバー空間 / モノドロミー / 実半単純Lie群 / Cartan部分環 / べき零Lie群 / 自由剛体 / 安定性解析 / Hamilton系 / 冪零Lie群 / Kummer曲面 / Maxwell方程式 / Lie環論 / 微分方程式 / quadriic line complex / Poisson力学系 / Birkhoff標準形 |
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| Outline of Final Research Achievements |
This research has dealt with various geometric structures arising from the Hamiltonian systems, which for example give a mathematical description of the rotational motion of a rigid body or the motion of a pendulum. The aim of the research is to reveal new geometric structures and to clarify the properties of dynamical systems geometrically. Particularly, one has considered the completely integrable Hamiltonian systems on Lie groups, which are Hamiltonian systems with the largest symmetry over the geometric object generalizing the rotation groups. As a result, one has clarified the stability properties of the equilibria for these systems. One has also revealed the geometric structures of elliptic fibrations arising from completely integrable systems of free rigid body dynamics in relation with the dynamical properties of the systems.
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