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.

2009y：我们得出对于某些超越整函数，“转数为有界型的西格尔圆盘的边界是拟圆”。作为推论，我们得到这些超越整函数的对数升力具有一个边界为拟圆的游走域。2010y：我们构造了一些超越整函数，满足“旋转数为有界型的西格尔盘的边界是拟圆” ”。我们在涉及动力学的所有完整函数的集合上引入了拓扑，并研究了关于拓扑的小扰动的西格尔圆盘的变化。2011y：我们理解了微分方程定性理论与复动力学之间的关系，并且我们研究了（超级）吸引复杂动力学的周期点、抛物线周期点、Siegel 点和 Cremer 点以及微分方程的平衡点。