Bounded Fatou components of transcendental entire functions with order less than 1/2

Yang, Cun Ji; Li, Yu Hua

doi:10.1007/s10114-015-3698-6

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2024

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“…Baker [41] 在 20 世纪 80 年代初问: 当超越整函数 f 的增长级充分小时, 是否蕴涵着 f 的 Fatou 分支都是有界的? 对于这个问题, Baker、Stallard、乔建永、Anderson-Hinkkanen、华歆厚 -杨重骏、郑建华、王跃飞、Rippon-Stallard、杨存基 -李玉华和 Nicks-Rippon-Stallard 等都进行了研究 (参见文献 [537,753,768] 及其中的参考文献).…”

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A brief introduction to one-dimensional complex dynamics

Fei

2024

Sci. Sin.-Math.

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. 1879 年, Cayley [168] 建议用该方法求解复多项式的根. 但他发现这个问题即使对于三次复多项式也已经非常困难: "The case of the cubic equation appears to present considerable difficulty." 从今天的视角来看, Cayley 在那时遇到困难是不可避免的, 因为他要解决的问题是计算一个三次有理函数的 Julia 集 (见图 1).Cayley 并不是第一个在 19 世纪 70 年代研究迭代的人. Schröder 在 1870-1871 年也考虑了用迭代法解方程, 同时还对下面的 Schröder 方程做了研究 3) :1884 年, Koenigs [416] 证明了如果导数 (或称 "乘子") λ = f ′ (0) 满足 |λ| ̸ =

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Section: 其他结论unclassified

A brief introduction to one-dimensional complex dynamics

Fei

2024

Sci. Sin.-Math.

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Bounded Fatou components of transcendental entire functions with order less than 1/2

Cited by 1 publication

References 19 publications

A brief introduction to one-dimensional complex dynamics

A brief introduction to one-dimensional complex dynamics

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