2017 Fiscal Year Final Research Report
study on geometric structures arising from dynamical systems
| 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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| 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 |
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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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| Free Research Field |
可積分系の理論，幾何学的力学系理論，および関連する幾何学（代数的・複素解析的幾何学等）
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