2007 Fiscal Year Final Research Report Summary
Analytic study of Painleve equations and a nelated clans of equation
| Project/Area Number |
17340050
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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 |
Global analysis
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| Research Institution | Keio University |
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Principal Investigator |
SHIMOMURA Shun Keio University, Facualry of Science and Technlogy, Prof. (00154328)
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| Co-Investigator(Kenkyū-buntansha) |
TANI Atusi Keio University, Faculty of Science and Technology, Prof (90118969)
SHIOKAWA Iekata Keio University, Faculty of Science and Technology, Honorary Prof (00015835)
KIMURA Hironobu Kumamoto University, Faculty of Science and Technology, Professor (40161575)
HANAOKA Yoshishige Kumamoto University, Faculty of Science and Technology, Professor (30208665)
ISHIGAKI Katsuya Nippon Insitute of Technology, Faculty of Engineering, Associate Professor (60202991)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Painleve equations / Ganier system / quasi-Painleve property / Fibonacci numbers |
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| Research Abstract |
1. We found a class of nonlinear ordinary differential equations containing the first Painleve equation such that each equation admits the quasi-Painleve property, and discussed the global multi-valuedness of their solutions. We also found a similar clean of equations containing the second Painleve equation.
2. For solutions of the fifth Painleve equation, we examined value distribution in a sectonial domain. Under a certain condition, we proved the equi-distribution of values.
3. For a degenerate Garnier system corresponding to the first Painleve equation, we obtain an asymptotic solution around a singular locus.
4. We examined algebraic independence and algebraic relations for reciprocal rums of Fibonacci numbers. We also discussed their relation to zeta values.
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