A new type of non-landing exponential rays

Jianxun Fu; Song Zhang

doi:10.3934/dcds.2020177

Article Contents

2020, Volume 40, Issue 7: 4179-4196. Doi: 10.3934/dcds.2020177

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A new type of non-landing exponential rays

Jianxun Fu^1, and
Song Zhang^2, ,

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
^* Corresponding author: Song Zhang

Received: April 2019

Revised: January 2020

Published online: July 2020

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).

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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.

Keywords:

Mathematics Subject Classification: Primary: 37F45; Secondary: 37F10.

Citation:

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Figure 1. 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 $

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Figure 2. 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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