论文标题
四式方程的渐近溶液
Asymptotic Solutions of the Tetration Equation
论文作者
论文摘要
在本报告中，我们构建了一个全态函数系列$β_{λ，μ}（s）$，其行为像$ | s |一样渐近地表现出渐近的指数。 \ to \ to \ infty $在右半平面中。每个$β_{λ，μ} $满足与嵌套指数的方便功能关系；并具有一系列扩展，以半平面收敛。它们提供了与地图$ e^{μz}的动力学相近：\ mathbb {c} \ to \ mathbb {c} $，并且随着分数迭代的行为而行为渐近。 这些对象用于描述指数函数的各种轨道。我们描述亚伯方程可从$β$构造的位置。在存在$2πi /λ$的时刻造成的，这是$ t $ t（s+1）= e^{μt（s）} $的全态亚伯函数。
In this report we construct a family of holomorphic functions $β_{λ,μ} (s)$ which behave asymptotically like iterated exponentials as $|s| \to \infty$ in the right half plane. Each $β_{λ,μ}$ satisfies a convenient functional relationship with nested exponentials; and has a series expansion that converges in a half-plane. They provide a nearness to the dynamics of the map $e^{μz} : \mathbb{C}\to\mathbb{C}$ and behave asymptotically as a fractional iteration would behave. These objects are used to describe the various orbits of the exponential function. We describe where Abel equations are feasibly constructed from $β$. Where there exists wildly holomorphic functions with period $2 πi / λ$ that are holomorphic Abel functions of the form $t(s+1) = e^{μt(s)}$.
