Combinatorial Dynamics And Entropy In Dimension One (2nd Edition)
Oct 2000 · Advanced Series In Nonlinear Dynamics Book 5 · World Scientific Publishing Company
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432
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About this ebook
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.
About the author
LluÃs Alsedà (Universitat Autònoma de Barcelona);Jaume Llibre (Universitat Autònoma de Barcelona);Michal Misiurewicz (Indiana University)
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