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.
- ISBN13 9789810240530
- Publish Date 1 November 2000
- Publish Status Active
- Publish Country SG
- Imprint World Scientific Publishing Co Pte Ltd
- Edition e
- Format Hardcover
- Pages 432
- Language English
- URL https://worldscientific.com/worldscibooks/10.1142/4205