Stability in the family of \(\omega \)-limit sets of alternating systems

DOI10.1016/j.jmaa.2011.12.056zbMath1246.37060OpenAlexW2058960324MaRDI QIDQ764959

Timothy H. Steele, D'Aniello, Emma

Publication date: 16 March 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.12.056

zbMATH Keywords

\(\omega\)-limit setalternating systemtypical behavior

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (6)

Equi-Baire one family of functions on metric spaces: a generalization of equi-continuity; and some applications ⋮ On chain recurrent sets of typical bounded Baire one functions ⋮ The structure of \(\omega\)-limit sets of asymptotically non-autonomous discrete dynamical systems ⋮ Computing topological entropy for periodic sequences of unimodal maps ⋮ Advances in Periodic Difference Equations with Open Problems ⋮ Spectral invariants of periodic nonautonomous discrete dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chaos in terms of the map \(x\to\omega(x,f)\)
• An extension of Sharkovsky's theorem to periodic difference equations
• On the periodic logistic equation
• Dynamics in one dimension
• Stability in the family of \(\omega \)-limit sets of continuous maps of the interval
• Continuity structure of \(f\mapsto \cup _{x\in I}\omega (x,f)\) and \(f\mapsto \{\omega (x,f) : x\in I\}\)
• The essential point set of a continuous function.
• 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
• Global Dynamics of Some Periodically Forced, Monotone Difference Equations
• The ω-limit sets of alternating systems
• Stability of dynamical structures under perturbation of the generating function
• Pitchfork bifurcation for non-autonomous interval maps
• The structure of $\omega$-limit sets for continuous maps of the interval
• Dynamics of Typical Continuous Functions
• The space of $\omega $-limit sets of a continuous map of the interval
• Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures
• Periodic structure of alternating continuous interval maps
• Approximating \(\omega\)-limit sets with periodic orbits

This page was built for publication: Stability in the family of \(\omega \)-limit sets of alternating systems