Pub. Date:
Springer Berlin Heidelberg
Dynamics in One Dimension / Edition 1

Dynamics in One Dimension / Edition 1

by Louis S. Block, William A. Coppel


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The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed.
Although most of the results were unknown thirty years ago,
the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour.

Product Details

ISBN-13: 9783540553090
Publisher: Springer Berlin Heidelberg
Publication date: 09/18/1995
Series: Lecture Notes in Mathematics , #1513
Edition description: 1. Aufl. 1992. Nachdruck 1995
Pages: 252
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Periodic orbits.- Turbulence.- Unstable manifolds and homoclinic points.- Topological dynamics.- Topological dynamics (continued).- Chaotic and non-chaotic maps.- Types of periodic orbits.- Topological Entropy.- Maps of the circle.

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