Author:
Block Louis,Coven Ethan M.
Abstract
AbstractLet 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)≠.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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