2009 Fiscal Year Final Research Report
Integrable system and monodromy
| Project/Area Number |
19740089
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Yokohama City University |
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Principal Investigator |
TAKEMURA Kouichi Yokohama City University, 国際総合科学部, 准教授 (10326069)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 可積分系 / モノドロミー / ホインの微分方程式 / ミドルコンボルーション / パンルベ方程式 / 初期値空間 / Hermite-Krichever仮設法 |
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| Research Abstract |
Heun's differential equation is a standard form of Fuchsian differential equations of second order which have four regular singularities. We studied solutions and monodromy of Heun's differential equation and its generalizations from a viewpoint of integrable system. In particular, we found unexplored solutions of Heun's differential equation by applying middle convolution, which is a transformation of differential equations, and we studied monodromy of the solutions. Moreover we clarified a relationship between Heun's differential equation and the space of initial conditions of the sixth Painleve equation.
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