Shift spaces and distributional chaos |
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| Affiliation: | 1. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 39, 30-059 Kraków, Poland;2. Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland;1. School of Science, Wuhan University of Technology, Wuhan 430070, China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;1. University of Hagen, Department of Economics, Universitaetsstrasse 41, 58097 Hagen, Germany;2. University of Hannover, School of Economics and Management, Koenigsworther Platz 1, 30167 Hannover, Germany;1. IRMAR, INSA de Rennes, 35708 Rennes, France;2. LAMA, Université Paris-Est Créteil, 94010 Créteil, France;1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Via per Arnesano, I-73100 LECCE, Italy;2. Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, I-43124 PARMA, Italy |
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| Abstract: | We give sufficient conditions for a shift to be distributionally chaotic and chaotic in the sense of Li and Yorke. In the case of cocyclic shifts we show the equivalence between distributional chaos, chaos in the sense of Li and Yorke, positivity of entropy and uncountability of subshift. |
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