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Maximum Entropy of Cycles of Even Period
 
Deborah M. King University of New South Wales, Sydney, NSW, Australia
John B. Strantzen La Trobe University, Bundoora, Victoria, Australia
Maximum Entropy of Cycles of Even Period
eBook ISBN:  978-1-4704-0316-4
Product Code:  MEMO/152/723.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
Maximum Entropy of Cycles of Even Period
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Maximum Entropy of Cycles of Even Period
Deborah M. King University of New South Wales, Sydney, NSW, Australia
John B. Strantzen La Trobe University, Bundoora, Victoria, Australia
eBook ISBN:  978-1-4704-0316-4
Product Code:  MEMO/152/723.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1522001; 59 pp
    MSC: Primary 37;

    A finite fully invariant set of a continuous map of the interval induces a permutation of that invariant set. If the permutation is a cycle, it is called its orbit type. It is known that Misiurewicz-Nitecki orbit types of period \(n\) congruent to \(1 \pmod 4\) and their generalizations to orbit types of period \(n\) congruent to \(3 \pmod 4\) have maximum entropy amongst all orbit types of odd period \(n\) and indeed amongst all \(n\)-permutations for \(n\) odd. We construct a family of orbit types of period \(n\) congruent to \(0\pmod 4\) which attain maximum entropy amongst \(n\)-cycles.

    Readership

    Graduate students and research mathematicians interested in dynamical systems and ergodic theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Some useful properties of the induced matrix of a maximodal permutation
    • 4. The family of orbit types
    • 5. Some easy lemmas
    • 6. Two inductive lemmas
    • 7. The remaining case
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1522001; 59 pp
MSC: Primary 37;

A finite fully invariant set of a continuous map of the interval induces a permutation of that invariant set. If the permutation is a cycle, it is called its orbit type. It is known that Misiurewicz-Nitecki orbit types of period \(n\) congruent to \(1 \pmod 4\) and their generalizations to orbit types of period \(n\) congruent to \(3 \pmod 4\) have maximum entropy amongst all orbit types of odd period \(n\) and indeed amongst all \(n\)-permutations for \(n\) odd. We construct a family of orbit types of period \(n\) congruent to \(0\pmod 4\) which attain maximum entropy amongst \(n\)-cycles.

Readership

Graduate students and research mathematicians interested in dynamical systems and ergodic theory.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Some useful properties of the induced matrix of a maximodal permutation
  • 4. The family of orbit types
  • 5. Some easy lemmas
  • 6. Two inductive lemmas
  • 7. The remaining case
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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