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

• Autorzy: Emma D’Aniello , Timothy Steele
• 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

EN

Cantor space; Continuous self-map; ω-limit set; Chaos

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B99: None of the above, but in this section
• 37B10: Symbolic dynamics

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 4
• Strony: 584-592

Daty

wydano

2014-04-01

online

2014-01-17

Twórcy

autor

Emma D’Aniello

• Seconda Università degli Studi di Napoli

autor

Timothy Steele

• Weber State University

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Identyfikatory

DOI

10.2478/s11533-013-0360-3