Chris Preston (auth.)9780387503295, 0-387-50329-3
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. |
Table of contents :
Introduction….Pages 1-19
Piecewise monotone mappings….Pages 20-33
Proof of Theorems 2.4 and 2.5….Pages 34-40
Sinks and homtervals….Pages 41-49
Examples of register-shifts….Pages 50-56
A proof of Parry’s theoren (Theorem 2.6)….Pages 57-67
Reductions….Pages 68-81
The structure of the set D(f)….Pages 82-102
Countable closed invariant sets….Pages 103-111
Extensions….Pages 112-125
Refinements….Pages 126-134
Mappings with one turning point….Pages 135-152
Some miscellaneous results from real analysis….Pages 153-159 |
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