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2014 | 12 | 4 | 584-592
Tytuł artykułu

Chaotic behaviour of the map x ↦ ω(x, f)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let K(2ℕ) be the class of compact subsets of the Cantor space 2ℕ, furnished with the Hausdorff metric. Let f ∈ C(2ℕ). We study the map ω f: 2ℕ → K(2ℕ) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2ℕ). The relationships between the continuity of ω f and some forms of chaos are investigated.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
4
Strony
584-592
Opis fizyczny
Daty
wydano
2014-04-01
online
2014-01-17
Twórcy
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0360-3
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