Elucidation of the boundary of various Siegel disks influenced by continued fraction expansions

阐明受连分式展开影响的各种西格尔圆盘的边界

• 批准号: 21740121
• 负责人: KATAGATA Koh
• 金额: $ 1.75万
• 依托单位: Ichinoseki National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740121/
• 关键词: 複素力学系; ジーゲル円板; 連分数展開

2009y : We obtained that for some transcendental entire functions,"the boundary of Siegel disks whose rotation number was of bounded type was a quasicircle". We obtained that the logarithmic lift of these transcendental entire functions had a wandering domain whose boundary was a quasicircle as a corollary.2010y : We constructed some transcendental entire functions satisfying that "the boundary of Siegel disks whose rotation number was of bounded type was a quasicircle". We introduced a topology on the set of all entire functions respecting dynamics and we studied variation of Siegel disks for small perturbation with respect to the topology.2011y : We comprehended the relationship between the qualitative theory of differential equations and complex dynamics, and we studied that(super) attracting periodic points, parabolic periodic points, Siegel points and Cremer points for complex dynamics and equilibrium points for differential equations.

2009年：我们获得了一些先验整个功能，“旋转数为有界类型的Siegel磁盘的边界为Quasicircle”。我们获得了这些先验的整个功能的对数提升具有一个流浪的域，其边界是推论的Quasicircle.2010y：我们构建了一些超越整个功能，满足了“ Siegel磁盘的边界，其旋转数为Quasicircle， ”。我们引入了有关尊重动态的所有功能的集合的拓扑，我们研究了Siegel磁盘的变化，以实现小扰动。 （超级）吸引周期点，抛物线周期点，siegel点和针对差分方程的复杂动力学和平衡点的火化点。