Distributional chaos and irregular recurrence |
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Authors: | Lenka Obadalová |
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Institution: | Mathematical Institute, Silesian University, CZ-746 01 Opava, Czech Republic |
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Abstract: | For a continuous map φ:X→X of a compact metric space, we study relations between distributional chaos and the existence of a point which is quasi-weakly almost periodic, but not weakly almost periodic. We provide an example showing that the existence of such a point does not imply the strongest version of distributional chaos, DC1. Using this we prove that, even in the class of triangular maps of the square, there are no relations to DC1. This result, among others, contributes to the solution of a problem formulated by A.N. Sharkovsky in the eighties. |
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Keywords: | primary 37B20 37D45 secondary 37B40 |
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