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Classification of permutations and cycles of maximum topological entropy

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Abstract

Iff is a continuous self-map of a compact interval we can represent each finite fully invariant set off by a permutation. We can then calculate the topological entropy of the permutation. This provides us with a numerical measure of complexity for any map which exhibits a given permutation type. In this paper we present cyclic and noncyclic permutations which have maximum topological entropy amongst all cyclic or noncyclic permutations of the same length.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Melbourne, 3010, Vic, Australia

    Deborah M. King

  2. School of Mathematical and Statistical Sciences, La Trobe University, 3086, Vic, Australia

    John B. Strantzen

Authors
  1. Deborah M. King
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  2. John B. Strantzen
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Correspondence to Deborah M. King.

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Supported by ARC grant F10007415.

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King, D.M., Strantzen, J.B. Classification of permutations and cycles of maximum topological entropy. Qual. Th. Dyn. Syst. 4, 77–97 (2003). https://doi.org/10.1007/BF02972824

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