| 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)
|
|---|
| 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.
|
