
Iterates of Piecewise Monotone Mappings on an Interval
Chris Preston(Author)
Springer (Publisher)
Published on 12. October 1988
Book
Paperback/Softback
VIII, 172 pages
978-3-540-50329-3 (ISBN)
Description
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.
More details
Series
Edition
1988 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 172 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 11 mm
Weight
283 gr
ISBN-13
978-3-540-50329-3 (9783540503293)
DOI
10.1007/BFb0079769
Schweitzer Classification
Content
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.