Title | Combinatorial Dynamics and Entropy in Dimension One |
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Author/s | Lluís Alsedà, Jaume Llibre (Universitat Autònoma de Barcelona) & Michal Misiurewicz (Indiana University) |

Year | 2000 |

Publisher | World Scientific |

ISBN | 978-981-02-4053-0 |

Link |

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.