Triangular maps with all periods and no infinite \(\omega\)-limit set containing periodic points

DOI10.1016/J.TOPOL.2005.01.012zbMath1176.37010OpenAlexW2025265102MaRDI QIDQ818405

Jaroslav Smítal, Luigi Paganoni, Gian Luigi Forti

Publication date: 20 March 2006

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2005.01.012

zbMATH Keywords

\(\omega \)-limit setperiodic pointuniformly recurrent pointtriangular mapschaotic in the sense of Lie and Yorke

Mathematics Subject Classification ID

Topological entropy (37B40) Iteration of real functions in one variable (26A18) Topological dynamics of nonautonomous systems (37B55) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (10)

From a Floyd-Auslander minimal system to an odd triangular map ⋮ The life and mathematics of Jaroslav Smítal ⋮ On a class of functions of the interval with zero topological entropy ⋮ Strange distributionally chaotic triangular maps. III ⋮ A triangular map of type \(2^{\infty}\) with positive topological entropy on a minimal set ⋮ A note on a problem on ω-limit sets ofN–dimensional skew-product maps ⋮ Strange distributionally chaotic triangular maps. II ⋮ A triangular map with homoclinic orbits and no infinite \(\omega\)-limit set containing periodic points ⋮ Sharkovsky's program for the classification of triangular maps is almost completed ⋮ Asymptotical periodicity for analytic triangular maps of type less than \(2^\infty \)

Cites Work

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• Dynamics in one dimension
• Triangular maps non-decreasing on the fibers
• A characterization of ω-limit sets of maps of the interval with zero topological entropy
• On dynamics of triangular maps of the square
• On Sharkovsky's cycle coexistence ordering
• Dynamics of homeomorphisms on minimal sets generated by triangular mappings
• A zero topological entropy map with recurrent points not $F_\sigma $
• Strange triangular maps of the square
• ON THE STRUCTURE OF THE ω-LIMIT SETS FOR CONTINUOUS MAPS OF THE INTERVAL

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