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

Published online by Cambridge University Press:  19 June 2002

PETRA šINDELÁŘOVÁ
PETRA šINDELÁŘOVÁ
Affiliation:
Mathematical Institute, Silesian University in Opava, Bezručovo nám. 13, Opava, Czech Republic (e-mail: petra.sindelarova@math.slu.cz)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 947 - 949
Copyright
2002 Cambridge University Press

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