Collet / Eckmann Iterated Maps on the Interval as Dynamical Systems

1. Auflage 2009
ISBN: 978-0-8176-4927-2
Verlag: Birkhäuser Basel
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 259 Seiten

Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems . 'This book is a thorough and readable introduction to some aspects of the theory of one-dimensional dynamical systems…The kneading calculus of Milnor—Thurston receives its most accessible treatment to date in print…This is an important and beautiful exposition, both as an orientation for the reader unfamiliar with this theory and as a prelude to studying in greater depth some of the hard papers on the subject.' —Mathematical Reviews (Review of the original hardcover edition) 'This book provides a good survey of recent developments in the study of the dynamics of smooth self-maps on the interval. It…deals with a subject whose literature often appears in

Autoren/Hrsg.

Collet, Pierre

Eckmann, Jean-Pierre

Inhaltsverzeichnis

1;Table of Contents;7
2;Introduction;9
3;Part I Motivation and Interpretation;12
4;Part II Properties of Individual Maps;74
5;Part III Properties of One-Parameter;184
6;References;250
7;Index;256
8;List of Mathematival Symbols;259