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- catalog abstract ""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.".
- catalog contributor b12174482.
- catalog contributor b12174483.
- catalog contributor b12174484.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog 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.".
- catalog description "Includes bibliographical references (p. 365-401) and index.".
- catalog extent "xvi, 415 p. :".
- catalog identifier "9810240538".
- catalog isPartOf "Advanced series in nonlinear dynamics ; v. 5".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Singapore ; River Edge, NJ : World Scientific,".
- catalog subject "514/.322 21".
- catalog subject "Combinatorial dynamics.".
- catalog subject "Entropy.".
- catalog subject "Mappings (Mathematics)".
- catalog subject "QA611.5 .A46 2000".
- catalog title "Combinatorial dynamics and entropy in dimension one / Lluís Alsedà & Jaume Llibre, Michał Misiurewicz.".
- catalog type "text".