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Maximum Entropy of Cycles of Even Period
Deborah M. King, University of New South Wales, Sydney, NSW, Australia, and John B. Strantzen, La Trobe University, Bundoora, Victoria, Australia
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Memoirs of the American Mathematical Society
2001; 59 pp; softcover
Volume: 152
ISBN-10: 0-8218-2707-3
ISBN-13: 978-0-8218-2707-9
List Price: US$49 Individual Members: US$29.40
Institutional Members: US\$39.20
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 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

• 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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