Szczegóły publikacji
Opis bibliograficzny
Specification properties and dense distributional chaos / Piotr OPROCHA // Discrete and Continuous Dynamical Systems ; ISSN 1078-0947. — 2007 — vol. 17 no. 4, s. 821–833. — Bibliogr. s. 832–833, Abstr.
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 31551 |
|---|---|
| Data dodania do BaDAP | 2007-02-17 |
| Tekst źródłowy | URL |
| Rok publikacji | 2007 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Discrete and Continuous Dynamical Systems, Series A |
Abstract
The notion of distributional chaos was introduced by Schweizer and Smital in [Trans. Amer. Math. Soc., 344 (1994) 737] for continuous maps of a compact interval. Further, this notion was generalized to three versions d(1)C d(3)C for maps acting on general compact metric spaces (see e.g. [Chaos Solitons Fractals, 23 (2005) 1581]). The main result of [J. Math. Anal. Appl., 241 (2000) 181] says that a weakened version of the specification property implies existence of a two points scrambled set which exhibits a d(1)C version of distributional chaos. In this article we show that much more complicated behavior is present in that case. Strictly speaking, there exists an uncountable and dense scrambled set consisting of recurrent but not almost periodic points which exhibit uniform d(1)C versions of distributional chaos.
