2005 Fiscal Year Final Research Report Summary
Topology of Solutions of 1st order PDEs and web g
| Project/Area Number |
14340022
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Ochanomizu University |
|---|
Principal Investigator |
NAKAI Isao Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (90207704)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SUWA Tatsuo Niigata University, Institute of Science and Technology, Professor, 自然科学系, 教授 (40109418)
SATO Hajime Nagoya University, Graduate school of Mathmatics, Professor, 大学院・多元数理研究科, 教授 (30011612)
ASUKE Taro The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (30294515)
TAKEBE Takashi Ochanomizu University, Faculty of Science, 理学部, 助教授 (60240727)
MAJIMA Hideyuki Ochanomizu University, Faculty of Science, 理学部, 教授 (50111456)
|
|---|
| Project Period (FY) |
2002 – 2005
|
| Keywords | complex foliation / holomorphic diffeomorphism / web geometry / complex dynamics / ordinary differential equation |
|---|
| Research Abstract |
We found some nentrivial relations of formal diffeomorphisms of C fixing 0 by the following method. In order to expand words of two formal series in Z∈C, we used the well known Camphell-Hausdorff formula in Lie algebra theory in a generalized form. If all the coefficients are 0, the word in idmtically Z, thus we obtain a relation. The property that the relation holds choosing Taylor coefficients of two diffecs properly is a combinatorial condition on the word.
|
