Memoirs of the American Mathematical Society 2001; 59 pp; softcover Volume: 152 ISBN10: 0821827073 ISBN13: 9780821827079 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/152/723
 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. Readership Graduate students and research mathematicians interested in dynamical systems and ergodic theory. 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
