Devaney chaos plus shadowing implies distributional chaos

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.

accepted by Chaos

References in corpus (5)

• Recent development of chaos theory in topological dynamics
• Stable sets and mean Li-Yorke chaos in positive entropy systems
• On $n$-scrambled tuples and distributional chaos in a sequence
• Two results on entropy, chaos, and independence in symbolic dynamics
• Shadowing property, weak mixing and regular recurrence