A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set

DOI10.1016/j.chaos.2014.11.012zbMath1351.37061OpenAlexW2064124915MaRDI QIDQ728166

Xiaoping Ou, Yuelin Gao, Lidong Wang

Publication date: 19 December 2016

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2014.11.012

zbMATH Keywords

distributionally scrambled setnoncompact weakly mixing dynamical system

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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Distributional chaos occurring on the set of proper positive upper Banach density recurrent points of one-sided symbolic systems

Cites Work

• A chaotic function with a distributively scrambled set of full Lebesgue measure
• A note on the map with the whole space being a scrambled set
• Homeomorphisms with the whole compacta being scrambled sets
• Distributional chaos revisited
• Invariant scrambled sets and distributional chaos
• There are no chaotic mappings with residual scrambled sets
• Period Three Implies Chaos
• Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval