Fractal attractors induced by β-shifts

被引：0
|
作者：
Neunhauserer, Joerg [1 ]
机构：
[1] Leibnitz Univ Hannover, Hannover, Germany
来源：
CHAOS SOLITONS & FRACTALS | 2019年 / 123卷
关键词：
beta-shift; Attractor; Symbolic dynamics; Fractals; Dimension; Entropy;
D O I：
10.1016/j.chaos.2019.03.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe a class of fractal attractors induced by beta-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log beta and have an ergodic measure of full entropy. This demonstrates that, symbolic dynamics can be used to determine significant properties of a geometric model in chaotic dynamics. Moreover we determine the Hausdorff dimension of the attractor induced by beta-shifts. Since the dimension is in (1,2) these attractors are fractals, we have thus found a new class of fractal attractors in the theory of dynamical systems. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：87 / 90
页数：4
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