A note on the map with the whole space being a scrambled set

DOI10.1016/j.na.2008.03.024zbMath1170.37010OpenAlexW2092005756MaRDI QIDQ1004644

Gongfu Liao, Qinjie Fan, Hui Wang

Publication date: 11 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.024

zbMATH Keywords

distal pairSchweizer-Smital pairSchweizer-Smital scrambled set

Mathematics Subject Classification ID

Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items

Mixing invariant extremal distributional chaos ⋮ COMPACT SYSTEMS WITH DC3 PAIRS ⋮ Cardinalities of scrambled sets and positive scrambled sets ⋮ Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets ⋮ Distributionally scrambled set and minimal set ⋮ A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set

Cites Work

• Unnamed Item
• A chaotic function with a distributively scrambled set of full Lebesgue measure
• Homeomorphisms with the whole compacta being scrambled sets
• A Chaotic Function with Some Extremal Properties
• A Chaotic Function Possessing a Scrambled Set with Positive Lebesgue Measure
• A Chaotic Function with a Scrambled Set of Positive Lebesgue Measure
• On Scrambled Sets for Chaotic Functions
• Period Three Implies Chaos
• Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval