Franklin

Iterates of Piecewise Monotone Mappings on an Interval [electronic resource] / by Chris Preston.

Author/Creator:
Preston, Christopher author., Author,
Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.
Format/Description:
Book
1 online resource (VIII, 172 pages)
Series:
Lecture Notes in Mathematics, 0075-8434 ; 1347
Lecture Notes in Mathematics, 0075-8434 ; 1347
Contained In:
Springer eBooks
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Subjects:
Mathematics.
Local subjects:
Real Functions. (search)
System Details:
text file PDF
Summary:
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.
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.
Contributor:
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
9783540459712
Publisher Number:
10.1007/BFb0079769 doi
Access Restriction:
Restricted for use by site license.