On Dynamics of Triangular Maps of the Square with Zero Topological Entropy

Abstract

It is known that, for interval maps, zero topological entropy is equivalent with bounded topological sequence entropy as well as with the non-existence of Li–Yorke scrambled triples. In this paper we answer the question how the situation changes when triangular maps of the unit square are concerned instead of interval maps.

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Acknowledgements

The research was supported by Grant SGS/18/2016 from the Silesian University in Opava. Support of this institution is gratefully acknowledged. The author thanks his supervisor Professor Marta Štefánková for valuable suggestions and comments.

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Correspondence to Vojtěch Pravec.

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Pravec, V. On Dynamics of Triangular Maps of the Square with Zero Topological Entropy. Qual. Theory Dyn. Syst. 18, 761–768 (2019). https://doi.org/10.1007/s12346-018-00311-7

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Keywords

  • Triangular maps
  • Topological entropy
  • Topological sequence entropy
  • LY-scrambled triple

AMS Subject Classification:

  • 54H20
  • 37B40
  • 37O45