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ω-limit sets for maps of the interval

Published online by Cambridge University Press:  19 September 2008

Louis Block  and
Ethan M. Coven
Louis Block
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
Ethan M. Coven
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA
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Abstract

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Let f denote a continuous map of a compact interval to itself, P(f) the set of periodic points of f and Λ(f) the set of ω-limit points of f. Sarkovskǐi has shown that Λ(f) is closed, and hence ⊆Λ(f), and Nitecki has shown that if f is piecewise monotone, then Λ(f)=. We prove that if x∈Λ(f)−, then the set of ω-limit points of x is an infinite minimal set. This result provides the inspiration for the construction of a map f for which Λ(f)≠.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 3 , September 1986 , pp. 335 - 344
Copyright
Copyright © Cambridge University Press 1986

References

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