2013 Fiscal Year Final Research Report
Study of structures of singular phenomena via complex global analysis
| Project/Area Number |
23540207
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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 | Hiroshima University |
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Principal Investigator |
YOSHINO Masafumi 広島大学, 理学(系)研究科(研究院), 教授 (00145658)
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| Project Period (FY) |
2011 – 2013
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| 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 |
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| 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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