Combinatorial Dynamics And Entropy In Dimension One (2nd Edition)
Author | : Luis Alseda |
Publisher | : World Scientific Publishing Company |
Total Pages | : 433 |
Release | : 2000-10-31 |
ISBN-10 | : 9789813105591 |
ISBN-13 | : 9813105593 |
Rating | : 4/5 (593 Downloads) |
Download or read book Combinatorial Dynamics And Entropy In Dimension One (2nd Edition) written by Luis Alseda and published by World Scientific Publishing Company. This book was released on 2000-10-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.