| Project/Area Number |
13650066
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Engineering fundamentals
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
UWANO Yoshio Kyoto University, Graduate School of Informatics, Associate Professor, 情報学研究科, 助教授 (80201953)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
IWAI Toshihiro Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (10021635)
山口 義幸 京都大学, 情報学研究科, 助手 (40314257)
|
|---|
| Project Period (FY) |
2001 – 2003
|
| Project Status |
Completed (Fiscal Year 2003)
|
| Budget Amount *help |
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥1,600,000 (Direct Cost: ¥1,600,000)
|
|---|
| Keywords | Birkhoff-Gustavson normalization / inverse problem / computer algebra / separation of variables / integrability of systems / algorithm / Birkhoff-Gustavson / 標準化 / 力学系 / 標準形 / 可積分系 / ハミルトン力学 / 国際情報交換 / ロシア / Bertrand-Darboux条件 |
|---|
| Research Abstract |
Application to the integrabilty of certain perturbed harmonic oscillators:
The separability the perturbed harmonic oscillators with homogeneous polynomial potentials of odd-degree, say δ, (the δ-PHOs for short) within rotations of the Cartesian coordinates is characterized as a necessary and sufficient condition for any δ-PHO to share its BG normal form with a (2δ -2)-PHO.
A necessary and sufficient condition for any 3-PHO to share its BG normal form with a 4-PHO in a linear magnetic field is obtained. A half of the 3-PHOs subject to the condition thus found are shown to be non-integrable through the Ziglin analysis. In the process of finding both of the results above, computer-algebra program ANFER developed by the head investigator are utilized very effectively.
Computer algebraic approach to the inverse problem:
The programs named ANFER and GITA^<-1> by the head investigator are unified into the new program GITAN. A faster program, named LINA, is written up by applying the Hori-Deprit transformation method to the inverse problem. This result is a part of the joint work with Dr.S.I. Vinitsky, the foreign collaborator of this project.
|
