There are no chaotic mappings with residual scrambled sets

DOI10.1017/S0004972700003695zbMath0646.26008OpenAlexW2010935965MaRDI QIDQ3789813

Tomáš Gedeon

Publication date: 1987

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700003695

zbMATH Keywords

scrambled setschaosperiodic point

Mathematics Subject Classification ID

Related Items (10)

Mixing invariant extremal distributional chaos ⋮ A mixing completely scrambled system exists ⋮ Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets ⋮ Rank 2 proximal Cantor systems are residually scrambled ⋮ Positive Measure Scrambled Sets of Some Chaotic Functions ⋮ A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set ⋮ ON INVARIANT ε-SCRAMBLED SETS ⋮ On the Lebesgue measure of Li-Yorke pairs for interval maps ⋮ Unnamed Item ⋮ Distributional chaos revisited

Cites Work

• 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
• Chaotic Functions with Zero Topological Entropy
• Period Three Implies Chaos

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