Invariant graphs of rational maps

Cui, Guizhen; Gao, Yan; Zeng, Jinsong

doi:10.1016/j.aim.2022.108454

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2024

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“…不变图为判定是否存在 Thurston 障碍提供了一条途径 (参见文献 [209,211]). 除了前文提到的 Newton 映射和 McMullen 映射, 扩张的 Thurston 映射 [118] 和临界有限有理函数 [203] 等也存在不变图.…”

Section: 拓扑刻画unclassified

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: 拓扑刻画unclassified

A brief introduction to one-dimensional complex dynamics

Fei

2024

Sci. Sin.-Math.

View full text Add to dashboard Cite

show abstract

Invariant graphs of rational maps

Cited by 1 publication

References 15 publications

A brief introduction to one-dimensional complex dynamics

A brief introduction to one-dimensional complex dynamics

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