Combinatorial Dynamics and Entropy in Dimension One (Advanced Series in Nonlinear Dynamics, V. 5) by Lluis Alseda
- Hardcover: 415 pages ISBN-13:
- ISBN-10: 9810240538
- Publisher: World Scientific Pub Co Inc; 2 Sub edition (February 2001)
- Series: Advanced Series in Nonlinear Dynamics, V. 5 (Book 5)
- Language: English
An introduction 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, and more; 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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