Study of connection problem for non-integrable Hamiltonian systems
Project/Area Number |
26400118
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
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Research Institution | Hiroshima University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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Keywords | ボレル総和法 / ハミルトン系 / 非可積分性 / 接続問題 / モノドロミー / Fuchsian equation / 特異摂動 / モーメント総話法 / semi formal solution / parametric Borel sum / semi-formal solution / Stokes phenomenon / Lotka Volterra / nonintegrability |
Outline of Final Research Achievements |
We study the structure of non-integrability of a Hamiltonian system and the global properties of solutions by using a singular first integral.The difficulty is to give the meaning to the divergent formal first integral or to the divergence of the normalizing transformation. We prove the Borel summability with respect to a certain parameter in the equation for first order system of partial differential equations. As for the non-integrability we show the semi-global non-integrability of a Hamiltonian system which is not analyzed by differential Galois theory. Because the global property of the first integral in the argument is not well understood, the result has the possibility to improve.
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Report
(4 results)
Research Products
(20 results)