Continuity of the maps \(f\mapsto\bigcup_{x\in I}\omega(x,f)\) and \(f\mapsto\{\omega(x,f):x\in I\}\)

DOI10.1155/IJMMS/2006/82623zbMath1130.37364MaRDI QIDQ884199

Timothy H. Steele

Publication date: 13 June 2007

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05)

Related Items (2)

A characterization of attractors for Baire functions on the interval ⋮ The persistence of \(\omega\)-limit sets defined on compact spaces

Cites Work

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• The persistence of \(\omega\)-limit sets under perturbation of the generating function.
• An \(\omega \)-limit set for a Lipschitz function with zero topological entropy
• Characterizations of Weakly Chaotic Maps of the Interval
• A Characterization of Nonchaotic Continuous Maps of the Interval Stable Under Small Perturbations
• Stability of dynamical structures under perturbation of the generating function
• Chaotic Functions with Zero Topological Entropy
• Periodic and Limit Orbits and the Depth of the Center for Piecewise Monotone Interval Maps
• The structure of $\omega$-limit sets for continuous maps of the interval
• A 𝐶¹ function for which the 𝜔-limit points are not contained in the closure of the periodic points
• The space of $\omega $-limit sets of a continuous map of the interval
• Density of periodic orbits in \(\omega \)-limit sets with the Hausdorff metric
• Iterative stability in the class of continuous functions

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