Combinatorial Dynamics And Entropy In Dimension One 2nd Edition
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Combinatorial Dynamics And Entropy In Dimension One (2nd Edition)
Author | : Luis Alseda |
Publisher | : World Scientific Publishing Company |
Total Pages | : 433 |
Release | : 2000-10-31 |
Genre | : Science |
ISBN | : 9813105593 |
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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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