The dynamics of a typical measurable function are determined on a zero measure set

zbMath1448.37035MaRDI QIDQ785254

Timothy H. Steele

Publication date: 6 August 2020

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rae/1593482446

zbMATH Keywords

\(\omega \)-limit settrajectorymeasurable function

Mathematics Subject Classification ID

Iteration of real functions in one variable (26A18) Dimension theory of smooth dynamical systems (37C45) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (2)

Dynamics of measurable functions on the interval ⋮ The easily bored sequence

Cites Work

• Graph theoretic structure of maps of the Cantor space
• Chaos among self-maps of the Cantor space
• On chain recurrent sets of typical bounded Baire one functions
• Chaos in terms of the map \(x\to\omega(x,f)\)
• Dynamics in one dimension
• Dynamics of typical Baire-1 functions on the interval
• The space of \(\omega\)-limit sets for Baire-1 functions on the interval
• A characterization of adding machine maps
• The space of adding machines generated by continuous self maps of manifolds
• Ubiquity of odometers in topological dynamical systems
• Continuity and chaos in discrete dynamical systems
• Dynamics of Typical Continuous Functions
• On Devaney's Definition of Chaos
• Liapunov stability and adding machines
• Dynamics of Typical Continuous Functions
• The space of $\omega $-limit sets of a continuous map of the interval
• On the sets of fixed points of bounded Baire one functions
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