Devaney chaos plus shadowing implies distributional chaos
Jian Li, Jie Li, Siming Tu
TL;DR
This paper demonstrates that in topological dynamical systems, the combination of Devaney chaos and shadowing property guarantees distributional chaos, linking different forms of chaotic behavior.
Contribution
It establishes that Devaney chaos plus shadowing implies distributional chaos, revealing a new connection among chaos types in dynamical systems.
Findings
Devaney chaotic systems with shadowing are distributionally chaotic
Connections among regional proximal, asymptotic, and distal relations are explored
The paper provides conditions under which chaos types imply each other
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.
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