2013 Fiscal Year Final Research Report
Rigidity and prolongability of differential equations and the study of global structure
| Project/Area Number |
21340038
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kumamoto University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
YOKOYAMA Toshiaki 千葉工業大学, 工学部, 教授 (30210636)
KATO Mitsuo 琉球大学, 教育学部, 教授 (50045043)
OSHIMA Toshio 城西大学, 理学部, 教授 (50011721)
TANABE Susumu Galatasaray 大学, 教授 (90432997)
KIMURA Hironobu 熊本大学, 大学院・自然科学研究科, 教授 (40161575)
SHIMENO Nobukazu 関西学院大学, 理工学部, 教授 (60254140)
SADAHIRO Taizo 津田塾大学, 学芸学部, 准教授 (00280454)
MIMACHI Katsuhisa 東京工業大学, 大学院・理工学研究科, 教授 (40211594)
KATO Fumiharu 熊本大学, 大学院・自然科学研究科, 教授 (50294880)
|
|---|
| Project Period (FY) |
2009-04-01 – 2014-03-31
|
| Keywords | 大域解析 / 複素領域における微分方程式 / モノドロミー / 完全積分可能系 / アクセサリー・パラメーター / 超曲面 / rigid局所系 / 接続係数 |
|---|
| Research Abstract |
We constructed a framework for the global study of linear ordinary differential equations and holonomic systems in several variables by using the notion of rigidity and spectral types and the operation called middle convolution. We succeeded to define the middle convolution for holonomic systems, which brings a new structure on the moduli space of holonomic systems. In some cases, middle convolution connects an ordinary differential equation to a holonomic system, and then we can compare various structures among ODEs and holonomic systems.
|
