A note on distributional chaos with respect to a sequence |
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Authors: | Piotr Oprocha |
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Affiliation: | aFaculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland |
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Abstract: | The aim of this note is to use methods developed by Kuratowski and Mycielski to prove that some more common notions in topological dynamics imply distributional chaos with respect to a sequence. In particular, we show that the notion of distributional chaos with respect to a sequence is only slightly stronger than the definition of chaos due to Li and Yorke. Namely, positive topological entropy and weak mixing both imply distributional chaos with respect to a sequence, which is not the case for distributional chaos as introduced by Schweizer and Smítal. |
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Keywords: | Distributional chaos Weak mixing Topological entropy |
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