On the invariance of Li–Yorke chaos of interval maps

DOI10.1080/10236190500138320zbMath1076.37024arXivmath/0610443OpenAlexW2024122106MaRDI QIDQ5317728

Bau-Sen Du

Publication date: 21 September 2005

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610443

zbMATH Keywords

symbolic dynamicsturbulent maps\(\delta\)-scrambled setssquare root construction

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Symbolic dynamics (37B10) Iteration of real functions in one variable (26A18) Dynamical systems involving maps of the interval (37E05)

Related Items

Invariant scrambled sets, uniform rigidity and weak mixing, On proximality with Banach density one, Cardinalities of scrambled sets and positive scrambled sets, An example of unbounded chaos, Syndetically proximal pairs, ON INVARIANT ε-SCRAMBLED SETS, Invariant scrambled sets and distributional chaos, On variants of distributional chaos in dimension one, Distributional chaos revisited, A dynamical version of the Kuratowski–Mycielski theorem and invariant chaotic sets, Invariance of distributional chaos for backward shifts, Recent development of chaos theory in topological dynamics

Cites Work

• Unnamed Item
• Dynamics in one dimension
• A Simple Proof of Sharkovsky's Theorem
• Every chaotic interval map has a scrambled set in the recurrent set
• Characterizations of Turbulent One-Dimensional Mappings Via ω-Limit Sets
• Period Three Implies Chaos