A characterization of ω-limit sets of maps of the interval with zero topological entropy

DOI10.1017/S0143385700007173zbMath0788.58021OpenAlexW2157987550MaRDI QIDQ3140473

Jaroslav Smítal, Andrew M. Bruckner

Publication date: 28 November 1993

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700007173

zbMATH Keywords

\(\omega\)-limit setzero topological entropyone dimensional map

Mathematics Subject Classification ID

Entropy in general topology (54C70) Low-dimensional dynamical systems (37E99)

Related Items (22)

Triangular maps with all periods and no infinite \(\omega\)-limit set containing periodic points ⋮ A zero topological entropy map with recurrent points not $F_\sigma $ ⋮ The dynamics of homeomorphisms of hereditarily decomposable chainable continua ⋮ A characterization of attractors for Baire functions on the interval ⋮ Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems ⋮ Strange triangular maps of the square ⋮ The life and mathematics of Jaroslav Smítal ⋮ Birkhoff centre and backward limit points ⋮ Why it is important to understand dynamics of triangular maps? ⋮ Unnamed Item ⋮ On open problems concerning distributional chaos for triangular maps ⋮ Self-similarity in the collection of \(\omega \)-limit sets ⋮ Minimal subsystems of triangular maps of type \(2^\infty\); conclusion of the sharkovsky classification program ⋮ Inhomogeneities in chainable continua ⋮ Strange distributionally chaotic triangular maps ⋮ Strange distributionally chaotic triangular maps. II ⋮ Sensitivity for set-valued maps induced by \(M\)-systems ⋮ Strong distributional chaos and minimal sets ⋮ ON THE STRUCTURE OF THE ω-LIMIT SETS FOR CONTINUOUS MAPS OF THE INTERVAL ⋮ On negative limit sets for one-dimensional dynamics ⋮ Dynamics of homeomorphisms on minimal sets generated by triangular mappings ⋮ Inheriting of chaos in uniformly convergent nonautonomous dynamical systems on the interval

Cites Work

• Chaos in terms of the map \(x\to\omega(x,f)\)
• Characterizations of Weakly Chaotic Maps of the Interval
• A Counterexample in Dynamical Systems of the Interval
• Chaotic Functions with Zero Topological Entropy
• Period Three Implies Chaos
• Simple Periodic Orbits of Mappings of the Interval

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