Analysis of an algebraic structure of a degenerate Garnier system from a viewpoint of algebraic solutions
Project/Area Number |
20540207
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Global analysis
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Research Institution | Mie University |
Principal Investigator |
KAWAMUKO Hiroyuki Mie University, 教育学部, 准教授 (00303719)
|
Project Period (FY) |
2008 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | ガルニエ系 / 有理解 / 代数解 / 差分パンルヴェ方程式 / モノドロミー保存変形 / 差分ガルニエ系 |
Research Abstract |
(1) We consider degenerate Garnier systems G(3,1,1) (which is defined by H.Kimura) and G(5/2,1,1) (which is defined by H.Kawamuko), and find all rational solutions of each equation. (2) We consider degenerate Garnier system G(3,2) (which is defined by H.Kimura), and find all algebraic solutions of G (3,2). (3) By using the results (1) and (2), we show that there is no birational transformation between these systems. (4) We consider a third order Fuchsian differential equation which has three regular singular points on Riemann sphere, and show that the Schlesinger transformation is equivalent to a difference VI Painlev\'e equation. Moreover, we can define a difference Garnier system in a similar way.
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Report
(4 results)
Research Products
(6 results)