Iterates of Piecewise Monotone Mappings on an Interval

1988
ISBN: 978-3-540-50329-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1347, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Preston, Chris

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Topologie Analytische Topologie

Inhaltsverzeichnis

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.