Every chaotic interval map has a scrambled set in the recurrent set

DOI10.1017/S0004972700002744zbMath0654.26005MaRDI QIDQ3800313

Bau-Sen Du

Publication date: 1989

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

zbMATH Keywords

periodic pointsscrambled setrecurrent pointsfunction chaotic in the sense of Li and Yorke

Mathematics Subject Classification ID

Iteration of real functions in one variable (26A18) Stability theory for smooth dynamical systems (37C75)

Related Items (4)

CHAOTIC MAP WITH THE PROPERTY OF RECURRENCE ⋮ On the invariance of Li–Yorke chaos of interval maps ⋮ Almost periodicity, chain recurrence and chaos ⋮ The set of recurrent points of a continuous self-map on an interval and strong chaos

Cites Work

• Interval maps, factors of maps, and chaos
• Chaos in \(C^ 0-\)endomorphism of interval
• 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
• On Scrambled Sets for Chaotic Functions
• Period Three Implies Chaos

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