A study on the dynamics of the family of complex cubic polynomials
| Project/Area Number |
17540177
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Polytechnic University |
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Principal Investigator |
NAKANE Shizuo Tokyo Polytechnic University, 工学部, 教授 (50172359)
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| Project Period (FY) |
2005 – 2008
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| Project Status |
Completed (Fiscal Year 2008)
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| Budget Amount *help |
¥3,060,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
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| 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 / parabolic locus / stretching map / Axiom A / polynomial skew product / 集積点集合 / pointwise accumulation set / Chebyshev写像 / 実biquadratic polynomials / bifurcation current / Branner-Hubbard deformation / central hyperbolic component / monodromy / Boettcher-Lavaurs vector / bifurcation measure |
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| 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。
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Report
(5 results)
Research Products
(25 results)
