2013 Fiscal Year Final Research Report
Asymptotic analysis for hypergeometric systems and Garnier systems
| Project/Area Number |
21340029
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
AOKI Takashi 近畿大学, 理工学部, 教授 (80159285)
KOIKE Tatsuya 神戸大学, 大学院・理学研究科, 准教授 (80324599)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 解析学 / 関数方程式論 / 漸近解析 / 代数解析 / 超幾何系 / ガルニエ系 / パンルヴェ階層 / ＷＫＢ解析 |
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| Research Abstract |
To generalize the exact WKB analysis to multidimensional problems, we consider completely integrable systems such as hypergeometric systems and Garnier systems from the viewpoint of the exact WKB analysis. We obtain the following fundamental results: "Coalescing phenomena of turning points" play an important role in determining the Stokes geometry of completely integrable systems as well as of higher order ordinary differential equations obtained as their restriction, in the case of linear completely integrable systems the Pearcey system gives a normal form at a point where a coalescing phenomenon of turning points occurs, and so on. Concerning the consolidation of the theory of exact WKB analysis, we also make a big progress in the analysis of the Voros coefficients of linear equations and Painleve equations by using the method of difference equations.
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