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On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property
- Source :
-
Chaos, Solitons & Fractals . Jun2011, Vol. 44 Issue 6, p429-432. 4p. - Publication Year :
- 2011
-
Abstract
- Abstract: Let X be a compact metric space and f: X → X be a continuous map. In this paper, we investigate the relationships between the asymptotic average shadowing property (Abbrev. AASP) and other notions known from topological dynamics. We prove that if f has the AASP and the minimal points of f are dense in X, then for any n ⩾1, f × f ×⋯× f(n times) is totally strongly ergodic. As a corollary, it is shown that if f is surjective and equicontinuous, then f does not have the AASP. Moreover we prove that if f is point distal, then f does not have the AASP. For f: [0,1]→[0,1] being surjective continuous, it is obtained that if f has two periodic points and the AASP, then f is Li–Yorke chaotic. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 44
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 60922483
- Full Text :
- https://doi.org/10.1016/j.chaos.2011.03.008