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y：我们得到了对某些超越整函数，“旋转数为有界型的Siegel圆的边界是拟圆”。我们得到了这些超越整函数的对数提升有一个边界为拟圆的游荡域作为花冠。2010y：我们构造了一些超越整函数，满足“旋转数为有界型的Siegel圆盘的边界为拟圆”。我们在所有关于动力学的整函数的集合上引入了一个拓扑，并且我们研究了Siegel圆盘在关于拓扑的小扰动下的变化。2011y：理解了微分方程定性理论与复动力学的关系，研究了（超）吸引周期点、抛物周期点、复动力学的Siegel点和Cremer点以及微分方程的平衡点。