On $n$-scrambled tuples and distributional chaos in a sequence

Abstract

The main aim of the present paper is to study relations between $n$-scrambled tuples and their attraction-adherence properties with respect to various sequences of integers. This extends previous research on relations between chaos in the sense of Li and Yorke and distributional chaos with respect to a given sequence. Moreover, we construct a system which is $n$-distributionally chaotic but not $(n+1)$-chaotic.

15 pages, to appear in J DIFFER EQU APPL

References in corpus (1)

• Chaos and Entropy for Interval Maps

Cited by in corpus (5)

• Recent development of chaos theory in topological dynamics
• Devaney chaos plus shadowing implies distributional chaos
• On "observable" Li-Yorke tuples for interval maps
• Corrigendum to "Syndetically proximal pairs" [J. Math. Anal. Appl. 379 (2011) 656--663]
• Scrambled and distributionally scrambled n-tuples