A study on the dynamics of the family of complex cubic polynomials

复三次多项式族动力学研究

• 批准号: 17540177
• 负责人: NAKANE Shizuo
• 金额: $ 1.96万
• 依托单位: Tokyo Polytechnic University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540177/
• 关键词: 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; po

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。

The theory of Branner-Hubbard-Lavaurus deformation of fixed points of objects is constructed, and the regularity of vibration of stretching rays and the discontinuity of stretching map are explained. The properties of Julia set of higher order polynomials are explained and new examples are given.

项目成果

Branner-Hubbard- Lavaurs deformations for real cubic poly- nomials with a parabolic fixed point.

具有抛物线不动点的实三次多项式的 Branner-Hubbard-Lavaurs 变形。

• DOI: 10.1090/s1088-4173-09-00192-1
• 发表时间: 2009
• 期刊: Conformal Geometry and Dynamics
• 影响因子: 0.6
• 作者: Toru Yanagawa;Shizuo Nakane;et.al.;Shizuo Nakane;Shizuo Nakane;Hiroyoshi Sasaki;Shizuo Nakane;Shizuo Nakane;Shizuo Nakane;Shizuo Nakane;Shizuo Nakane;Shizuo Nakane
• 通讯作者: Shizuo Nakane

An Axiom A polynomial skew product of degree four

An Axiom A 四次多项式偏斜积

• 发表时间: 2008
• 作者: Y. Kohsaka & T;Nagasawa;中根静男
• 通讯作者: 中根静男

Branner-Hubbard-Lavaurs motion of parabolic cubic polynomials

抛物三次多项式的 Branner-Hubbard-Lavaurs 运动

• 发表时间: 2005
• 作者: Y. Kohsaka & T;Nagasawa;Shizuo Nakane
• 通讯作者: Shizuo Nakane

On Axiom A polynomial skew products of higher degrees

关于 Axiom A 高阶多项式偏斜积

• 发表时间: 2008
• 作者: Fujiwara;D.and Kumano-go;N.;K. Asakura;Shizuo Nakane
• 通讯作者: Shizuo Nakane

Branner-Hubbard-Lavaurs deformation of parabolic cubic polynokmials

抛物三次多项式的 Branner-Hubbard-Lavaurs 变形

• 发表时间: 2006
• 作者: Y. Kohsaka & T;Nagasawa;中根静男;K.Yajima;Shizuo Nakane;D.Finco and K.Yajima;H. Kubo & M. Ohta;Shizuo Nakane;T.Kobayashi T.Suzuki and K.Watanabe;Shizuo Nakane;M. Ohta & G. Todorova;中根静男
• 通讯作者: 中根静男