eBook ISBN:  9781470403164 
Product Code:  MEMO/152/723.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 
eBook ISBN:  9781470403164 
Product Code:  MEMO/152/723.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 152; 2001; 59 ppMSC: 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 MisiurewiczNitecki 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.
ReadershipGraduate 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


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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 MisiurewiczNitecki 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.
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