Integrable system and monodromy
| Project/Area Number |
19740089
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Yokohama City University |
|---|
Principal Investigator |
TAKEMURA Kouichi Yokohama City University, 国際総合科学部, 准教授 (10326069)
|
|---|
| Project Period (FY) |
2007 – 2009
|
| Project Status |
Completed (Fiscal Year 2009)
|
| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
|
|---|
| Keywords | 可積分系 / モノドロミー / ホインの微分方程式 / ミドルコンボルーション / パンルベ方程式 / 初期値空間 / Hermite-Krichever仮設法 / 岡本の初期値空間 / Middle convolution / 積分表示 / 有限帯ポテンシャル / Hermite-Krichever仮説法 |
|---|
| Research Abstract |
Heun's differential equation is a standard form of Fuchsian differential equations of second order which have four regular singularities. We studied solutions and monodromy of Heun's differential equation and its generalizations from a viewpoint of integrable system. In particular, we found unexplored solutions of Heun's differential equation by applying middle convolution, which is a transformation of differential equations, and we studied monodromy of the solutions. Moreover we clarified a relationship between Heun's differential equation and the space of initial conditions of the sixth Painleve equation.
|
Report
(4 results)
Research Products
(20 results)
