Combinatorial Dynamics and Entropy in Dimension One, Vol. 5 FROM THE PUBLISHER
"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."--BOOK JACKET.
FROM THE CRITICS
Booknews
Written primarily for graduate students and researchers, this book introduces two of the main directions of one-dimensional dynamics. The first is a theory of combinational dynamics; it is based on the Sharkovski theorem. The second measures complexity and "chaos" by studying the topological entropy of a system. The book aims to provide a unified and detailed exposition of these developments for internal and circle maps. Chapters cover preliminaries, interval maps, circle maps, and entropy. Appendixes discuss graph maps and rotation theory. Alsed and Llibre teach at the Universitat Autnoma de Barcelona. Misiurewicz teaches at Indiana University and Purdue University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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