Combinatorial dynamics and entropy in dimension one
By: Lluís Alsedà & Jaume Llibre, Michał Misiurewicz.
Contributors: Llibre, Jaume.; Misiurewicz, Michał, 1948-
Edition: 2nd ed.
Series: Advanced series in nonlinear dynamics ;; v. 5
Publisher: World Scientific
Published: 2000
Place of publication: Singapore; River Edge, NJ
Language: eng
Number of pages: 415
Subjects: Combinatorial dynamics.; Mappings (Mathematics); Entropy.
Description: "This book introduces the reader to two of the main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all periodic orbits of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.: it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of "chaos" present in it. A good way of doing this is to study the topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. The second edition contains two new appendices, where an extension of the theory to tree and graph maps is presented without technical proofs."--Jacket.
Notes: Includes bibliographical references (p. 365-401) and index.