| Project/Area Number |
21540174
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
KISAKA Masashi 京都大学, 人間・環境学研究科(研究院), 准教授 (70244671)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
SHISHIKURA Mitsuhiro 京都大学, 大学院理学研究科, 教授 (70192606)
INOU Hiroyuki 京都大学, 大学院理学研究科, 講師 (00362434)
NAKANE Shizuo 東京工芸大学, 工学部, 教授 (50172359)
MOROSAWA Shunsuke 高知大学, 理学部, 教授 (50220108)
|
|---|
| Project Period (FY) |
2009-04-01 – 2014-03-31
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 超越整関数 / Julia集合 / Fatou集合 / 多項式 |
|---|
| Research Abstract |
We investigated the dynamics of polynomials and transcendental entire functions both individually and bidirectionally by mainly using complex analytic methods. As a remarkable result, for a given polynomial P we constructed a transcendental entire function which has the dynamics of P as its subdynamics by quasiconformal surgery. Also as an application of this method, we constructed, for example, (1)a transcendental entire function whose Julia set is a Sierpinski carpet, (2)a transcendental entire function which has a Cremer point but whose Julia set is locally connected. These are new examples which show new phenomena which never occur for polynomial dynamics.
|
