On open problems concerning distributional chaos for triangular maps |
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Authors: | F Balibrea J Smítal M Štefánková |
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Institution: | aUniversidad de Murcia, Departamento de Matemáticas, 30100 Murcia, Spain;bMathematical Institute, Silesian University, 746 01 Opava, Czech Republic |
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Abstract: | We show that in the class T of the triangular maps (x,y)?(f(x),gx(y)) of the square there is a map of type 2∞ with non-minimal recurrent points which is not DC3. We also show that every DC1 continuous map of a compact metric space has a trajectory which cannot be (weakly) approximated by trajectories of compact periodic sets. These two results make possible to answer some open questions concerning classification of maps in T with zero topological entropy, and contribute to an old problem formulated by A.N. Sharkovsky. |
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Keywords: | MSC: primary 37B05 37B20 37B40 37B55 54H20 |
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