2008 Fiscal Year Final Research Report
A study on the dynamics of the family of complex cubic polynomials
| Project/Area Number |
17540177
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Tokyo Polytechnic University |
|---|
Principal Investigator |
NAKANE Shizuo Tokyo Polytechnic University, 工学部, 教授 (50172359)
|
|---|
| Project Period (FY) |
2005 – 2008
|
| Keywords | Branner-Hubbard-Lavaurs deformation / stretching ray / straightening map / Axiom A polynomial skew product / base Julia set / fiber Julia set / point-wise accumulation set / component-wise accumulation set |
|---|
| Research Abstract |
放物的不動点を持つ3次多項式のBranner-Hubbard-Lavaurs deformationの理論を構築し、stretching raysの振動の規則性やstretching mapの不連続性を解明した。高次多項式のJulia setの性質を用いることにより、base Julia set が連結でないAxiom Apolynomial skew productの力学系について、特に危点集合の集積点集合の性質を解明し、新しい例を構成した。
|
