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Princeton University Library Catalog
Iterates of piecewise monotone mappings on an interval / edited by Chris Preston.
1st ed. 1988.
Berlin, Heidelberg : Springer-Verlag, 
1 online resource (VIII, 172 p.)
Iterative methods (Mathematics)
Preston, Christopher J.
Lecture notes in mathematics (Berlin) ; Volume 1347.
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Lecture Notes in Mathematics ; Volume 1347
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.
Bibliographic Level Mode of Issuance: Monograph
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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)
The structure of the set D(f)
Countable closed invariant sets
Mappings with one turning point
Some miscellaneous results from real analysis.
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Iterates of piecewise monotone mappings on an interval / Chris Preston.