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## Fundamenta Mathematicae

2012 | 217 | 1 | 35-54
Tytuł artykułu

### On the ω-limit sets of tent maps

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EN
For a continuous map f on a compact metric space (X,d), a set D ⊂ X is internally chain transitive if for every x,y ∈ D and every δ > 0 there is a sequence of points ⟨x = x₀,x₁,...,xₙ = y⟩ such that $d(f(x_i),x_{i+1})< δ$ for 0 ≤ i< n. In this paper, we prove that for tent maps with periodic critical point, every closed, internally chain transitive set is necessarily an ω-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an ω-limit set. Together, these results lead us to conjecture that for tent maps with shadowing, the ω-limit sets are precisely those sets having internal chain transitivity.
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Rocznik
Tom
Numer
Strony
35-54
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Daty
wydano
2012
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autor
• School of Mathematics, University of Bristol, Howard House, Queens Avenue, Bristol, BS8 1SN, UK
• School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
autor
• Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, UK
autor
• School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
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