2011 Fiscal Year Final Research Report
Studies on Painleve or Garnier systems by means of their phase spaces
| Project/Area Number |
21540224
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Aoyama Gakuin University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MASUDA Tetsu 青山学院大学, 理工学部, 准教授 (00335457)
MURATA Mikio 青山学院大学, 理工学部, 助教 (60447365)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 関数方程式の大域理論 / 関数論 / パンルヴェ系 / ガル二エ系 / 相空間 / 合流操作 / パンルヴェ性 |
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| Research Abstract |
The purpose of this assignment is to clarify the fundamental properties of Painleve or Garnier systems by means of their phase spaces. Garnier systems of two independent variables are defined corresponding to partitions of 5, and there exists confluence process between any two systems for the partitions one of which is adjacent to the other. The most important result of our study is to lift up the confluence processes to the level of phase spaces for Garnier systems of two variables. We have tried to prove the Painleve property for the degenerate Garnier systems of two variables by using the above result, but complete proof has not yet been obtained.
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