Maximum entropy of cycles of even period
Author(s)
Bibliographic Information
Maximum entropy of cycles of even period
（Memoirs of the American Mathematical Society, no. 723）
American Mathematical Society, 2001
Available at 14 libraries
Note
"July 2001, volume 152, number 723 (fourth of 5 numbers)"
Includes bibliographical references (p. 59)
Description and Table of Contents
Description
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.
Table of Contents
Introduction Preliminaries Some useful properties of the induced matrix of a maximodal permutation The family of orbit types Some easy lemmas Two inductive lemmas The remaining case References.
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