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Combinatorial Patterns for Maps of the Interval






Publisher:  American Mathematical Society
Summary: In recent years, motivated by Shrkovskii's theorem, researchers have realized that a good deal of information about the dynamics of a map on the interval can be deduced from the combinatorial structure of its periodic orbits. This data can be formulated as a "forcing" relation between cyclic permutations (representing "orbit types" of periodic orbits). The present study investigates a number of new features of this r...elation and its generalization to multicyclic permutations (modelling finite unions of periodic orbits) and combinatorial patterns (modelling finite invariant sets). A central theme is the role of reductions and extensions of permutations. Results include: (i) a "combinatorial shadowing theorem" and its application to approximating permutations by cycles in the forcing relation; (ii) the distribution of different representatives of a given cycle in one (adjusted) map; (iii) characterization of the forcing-maximal permutations and patterns of fixed degree; and (iv) a calculation of the asymptotic growth rate of the maximum entropy forced by a permutation of given degree.

Misiurewicz, Michael is the author of Combinatorial Patterns for Maps of the Interval, published under ISBN 9780821825136 and 0821825135. Three Combinatorial Patterns for Maps of the Interval textbooks are available for sale on ValoreBooks.com, two used from the cheapest price of $101.23, or buy new starting at $32.06.
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ISBN-13: 9780821825136

ISBN: 0821825135

Publisher: American Mathematical Society
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