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Devaney chaos plus shadowing implies distributional chaos

2016/09/01 by Jian Li, Jie Li, Siming Tu
Mathematics · Physics and Astronomy · #CHAOS (operating system) #Chaos control and synchronization #Chaotic #Dynamical system (definition) #Dynamical systems theory #Mathematical Dynamics and Fractals #Property (philosophy) #Quantum chaos and dynamical systems #Relation (database) #Topology (electrical circuits) #math.DS #msc:37B05 #msc:37C50 #msc:54H20

paper · pdf · doi:10.1063/1.4962131

published as Chaos 26, 093103 (2016); 6 pages · accepted by Chaos

openalex publication_date 2016/09/01 · arxiv created 2016/09/11 · openalex created_date 2016/09/16 · arxiv updated 2016/11/01 · openalex updated_date 2026/08/05

Abstract

We explore connections among the regional proximal relation, the asymptotic relation, and the distal relation for a topological dynamical system with the shadowing property and show that if a Devaney chaotic system has the shadowing property then it is distributionally chaotic.

Citations