Continuity and chaos in discrete dynamical systems

DOI10.1007/s00010-005-2813-7zbMath1092.37023OpenAlexW1991564044MaRDI QIDQ2494448

Timothy H. Steele

Publication date: 28 June 2006

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-005-2813-7

zbMATH Keywords

stabilitycontinuityperiodic orbitsHausdorff measure\(\omega\)-limit setinterval mapresidual set

Mathematics Subject Classification ID

Topological dynamics (37B99) Iteration of real functions in one variable (26A18) Dynamical systems involving maps of the interval (37E05)

Related Items (15)

Ubiquity of odometers in topological dynamical systems ⋮ Dynamics of measurable functions on the interval ⋮ Dynamics of typical Baire-1 functions on the interval ⋮ Iterates of Borel functions ⋮ Dynamics of Baire-1 functions on the interval ⋮ On the existence of maximal \(\omega \)-limit sets for dendrite maps ⋮ Dynamics of typical Baire-1 functions ⋮ Dynamics of typical Baire-1 functions on a compact \({n}\)-manifold ⋮ The space of adding machines generated by continuous self maps of manifolds ⋮ Asymptotically stable sets and the stability of \(\omega\)-limit sets ⋮ Prevalence and structure of adding machines for cellular automata ⋮ Stability in the family of \(\omega \)-limit sets of alternating systems ⋮ Dynamics of Baire-2 functions on the interval ⋮ The dynamics of a typical measurable function are determined on a zero measure set ⋮ The persistence of \(\omega\)-limit sets defined on compact spaces

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