# American Institute of Mathematical Sciences

July  2020, 40(7): 4179-4196. doi: 10.3934/dcds.2020177

## A new type of non-landing exponential rays

 1 Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Song Zhang

Received  April 2019 Revised  January 2020 Published  April 2020

Fund Project: This work is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2019kfyXJJS135) and the National Natural Science Foundation of China (Grant No. 11901219)

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.

Citation: Jianxun Fu, Song Zhang. A new type of non-landing exponential rays. Discrete & Continuous Dynamical Systems - A, 2020, 40 (7) : 4179-4196. doi: 10.3934/dcds.2020177
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##### References:
The folding process of $\gamma_{6}^0$ by $g_{1}^- \circ g_{2}^+ \circ \cdots\circ g_{5}^-\circ g_{6}^+$ for the above choice of $\xi_i$ with $i = 0,1,\cdots,5$
Here is the sketch of $\gamma_0^{-12}$. The black polylines with different-sized bold show the idea of how the limit curve $\eta$ is produced in the accumulation set of $\gamma_0$
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