A new type of non-landing exponential rays

Abstract

In this paper, we will construct a new type of non-landing exponential rays, each of whose accumulation sets is bounded, disjoint from the ray and homeomorphic to the closed topologist's sine curve.

A brief introduction to one-dimensional complex dynamics

“…除了上面提到的着陆逃逸曲线, 20 世纪 90 年代开始, Devaney 等构造了一些非着陆的逃逸曲线, 其聚点集为无界的不可分割连续统 (参见文献 [234,241,617]). 付建勋、张高飞和张松等构造了聚点集 有界且非着陆的逃逸曲线并研究了它们的拓扑结构 (参见文献 [314,315]). 关于超越亚纯函数 Julia 连 通分支的可能拓扑结构参见文献 [252,488,489,623].…”