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Maximal entropy of permutations of even order

  • DEBORAH M. KING

Abstract

A finite invariant set of a continuous map of an interval induces a permutation called its type. If this permutation is a cycle, it is called its orbit type. It has been shown by Geller and Tolosa that Misiurewicz–Nitecki orbit types of period $n$ congruent to $1$ (mod 4) and their generalizations to orbit types of period $n$ congruent to $3$ (mod 4) have maximal entropy among all orbit types of odd period $n$, and indeed among all permutations of period $n$. We further generalize this family to permutations of even period $n$ and show that they again attain maximal entropy amongst $n$-permutations.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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