Overview

Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.

Full Product Details

Author:   Chris Preston
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1988 ed.
Volume:   1347
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.580kg
ISBN:  

9783540503293

ISBN 10:   3540503293
Pages:   172
Publication Date:   12 October 1988
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Piecewise monotone mappings.- Proof of Theorems 2.4 and 2.5.- Sinks and homtervals.- Examples of register-shifts.- A proof of Parry's theoren (Theorem 2.6).- Reductions.- The structure of the set D(f).- Countable closed invariant sets.- Extensions.- Refinements.- Mappings with one turning point.- Some miscellaneous results from real analysis.

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