Combinatorial Dynamics and Entropy in Dimension One (Advanced Nonlinear Dynamics)

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9789810240530: Combinatorial Dynamics and Entropy in Dimension One (Advanced Nonlinear Dynamics)
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This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (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; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.

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"As a whole, the book is carefully written and contains a very detailed account of a body of material along with some new results. The book will serve as a valuable reference for those interested in the combinatorial aspects of one-dimensional dynamical systems." A Quas Mathematics Abstracts

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Other Popular Editions of the Same Title

9789810242305: Combinatorial Dynamics and Entropy in Dimension One

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ISBN 10:  9810242301 ISBN 13:  9789810242305
Publisher: World Scientific Pub Co Inc, 1993
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9789810213442: Combinatorial Dynamics and Entropy in Dimension One (Advanced Series in Nonlinear Dynamics)

World ..., 1993
Hardcover

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Book Description World Scientific Publishing Co Pte Ltd, Singapore, 2001. Hardback. Condition: New. 2nd ed. Language: English. Brand new Book. This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (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; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself. Seller Inventory # BTA9789810240530

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