Asymptotic analysis on the Painleve equations and monodromy problems
| Project/Area Number |
21540217
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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 | Osaka University |
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Principal Investigator |
OHYAMA Yousuke 大阪大学, 大学院・情報科学研究科, 准教授 (10221839)
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| Co-Investigator(Renkei-kenkyūsha) |
SAKAI Hidetaka 東京大学, 数理科学研究科, 准教授 (50323465)
KIMURA Hironobu 東京大学, 数理科学研究科, 教授 (40161575)
HARAOKA Yoshishige 東京大学, 数理科学研究科, 教授 (30208665)
TAKEMURA Koichi 中央大学, 理工学部, 准教授 (10326069)
KOIKE Tatsuya 神戸大学, 理学研究科, 准教授 (80324599)
MANO Toshiyuki 琉球大学, 理学部, 助教 (60378594)
KAWAMUKO Hiroyuki 三重大学, 教育学部, 准教授 (00303719)
KIKUCHI Tetsuya 青山学院大学, 理工学部, 非常勤講師 (00374900)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可積分系 / パンルヴェ方程式 / 漸近解析 / カルタン幾何 / q-パンルヴェ方程式 / 超幾何函数 / 代数函数 / モノドロミ / モノドロミ非保存変形 |
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| Research Abstract |
We study special solutions of the q-Painleve equations. In the case| q|=1, the first and the second q-Painleve equation has convergent solutions around the infinity. If q is a root of unity, they are represented by hypergeometric functions. We gave a coalescent diagram for q-hypergeometric functions and we obtain seven q-difference linear equations. For classical Painleve equations, we are studying convergence of asymptotic expansions. We also studied that monodromy evolving deformations for irregular singular cases.
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Report
(4 results)
Research Products
(32 results)
