Study of structures of singular phenomena via complex global analysis
Project/Area Number |
23540207
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Hiroshima University |
Principal Investigator |
YOSHINO Masafumi 広島大学, 理学(系)研究科(研究院), 教授 (00145658)
|
Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
Keywords | ハミルトン系 / 非可積分性 / モノドロミー / ボレル総和法 / モーメント総話法 / 特異摂動 / 完全漸近解析 / 超幾何方程式系 / モーメントボレル総和法 / 接続問題 / 超幾何方程式 / モーメント総和法 / 接続係数 / 不確定特異点 |
Research Abstract |
We have obtained the concrete formula of the monodromy of a certain confluent hypergeometric system which can be written in a Hamiltonian form. The method may be extended to more general system of equations and may be applied to the study of connection formulas near the irregular singular point. The method has some similarity to the so-called KAM theory. The other result of the research is the proof of the Borel summability of a singular perturbative formal solution of a certain a multi-dimensional Fuchsian equation. This results was proved in the case of one variable. Using the method in the above we have analyzed the analytic behavior of Lotoka Volterra system of three species with evolutional effect.
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Report
(4 results)
Research Products
(28 results)