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
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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.
by "Nielsen BookData"