The Hierarchy of Distributional Chaos-Reference-Cited by-同舟云学术

The Hierarchy of Distributional Chaos

Published:2015-01 Issue:01 Volume:25 Page:1550001
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Fu Heman¹,Xiong Jincheng²,Wang Huoyun³

Affiliation:

1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, P. R. China

2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China

3. Department of Mathematics, Guangzhou University, Guangzhou 510006, P. R. China

Abstract

For each λ ∈ [0, 1], λ-power distributional chaos has been defined via Furstenberg families to strengthen distributional chaos. For the sake of distinguishing them, we present a class of dynamical systems, called wedge-shape systems. Through a thorough analysis of dynamical behaviors of all point-pairs, we show that wedge-shape systems can be λ-power distributionally chaotic and admit no λ′-power distributionally scrambled pairs for any λ′ ∈ [0, λ). Then we unfold a picture of distributional chaos with rich hierarchical structures, which helps to improve our comprehension of the diversity of chaos.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127415500017

Reference9 articles.

1. Recurrence in Topological Dynamics

2. On distributionally chaotic and null systems

3. Homeomorphisms with the whole compacta being scrambled sets

4. Period Three Implies Chaos

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