Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
35-54
Opis fizyczny
Daty
wydano
2012
Twórcy
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
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-1-4