Perturbation problems for degenerate integrable systems and mathematics for resonance phenomena
| Project/Area Number |
25400108
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
Ito HIdekazu 金沢大学, 数物科学系, 教授 (90159905)
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| Co-Investigator(Kenkyū-buntansha) |
柴山 允瑠 京都大学, 情報学研究科, 准教授 (40467444)
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| Co-Investigator(Renkei-kenkyūsha) |
YAGASAKI Kazuyuki 京都大学, 情報学研究科, 教授 (40200472)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 可積分系 / 共鳴 / 超可積分系 / シンプレクティック写像 / 標準形理論 / 標準形 / ハミルトン系 / 可積分ベクトル場 / 超可積分性 / バーコフ標準形 |
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| Outline of Final Research Achievements |
We studied various problems concerning the global structure of solutions for integrable systems and superintegrable systems possessing larger number of integrals. The resonance among eigenvalues of linearized dynamics associated with invariant sets such as equilibria played an important role in this study. In particular, we studied an even dimensional analytic vector field near an elliptic equilibrium point and showed that there exists an analytic transformation which takes the vector field into Poincare-Dulac normal form, provided that there exist a sufficient number (associated with the resonance degree) of integrals and commuting vector fields. This gives an alternative proof of a known result under weaker assumptions in a special case. Also, we succeeded in showing that a superintegrable symplectic map can be taken analytically into Birkhoff normal form without assuming semi-simplicity of its linear part.
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Report
(5 results)
Research Products
(15 results)
