Stability of asymptotically stable sets for continuous functions

DOI10.1016/S0022-247X(02)00438-9zbMath1015.26011MaRDI QIDQ1856980

Roy A. Mimna, Timothy H. Steele

Publication date: 11 February 2003

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

zbMATH Keywords

semicontinuityattractorasymptotically stable set

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Iteration of real functions in one variable (26A18) Dynamical systems involving maps of the interval (37E05)

Cites Work

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• The space of dynamical systems with the \(C^ 0\)-topology
• 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 \(f\mapsto \{\omega (x,f) : x\in I\}\)
• Points generating the principal measure of chaos
• Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval
• The space of $\omega $-limit sets of a continuous map of the interval
• Iterative stability in the class of continuous functions

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