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A zero topological entropy map for which periodic points are not a G_\delta set

  • PETRA šINDELÁŘOVÁ (a1)

Abstract

We exhibit an example of a continuous map of the interval of type 2^\infty, and hence of zero topological entropy, for which the set of periodic points is not a G_\delta set. This disproves a conjecture by Sharkovsky from 1965. Unfortunately, this conjecture has been incorrectly quoted as a true statement by other authors in many papers and books.

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A zero topological entropy map for which periodic points are not a G_\delta set

  • PETRA šINDELÁŘOVÁ (a1)

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