Iterates of piecewise monotone mappings on an interval / edited by Chris Preston.

Format
Book
Language
English
Εdition
1st ed. 1988.
Published/​Created
  • Berlin, Heidelberg : Springer-Verlag, [1988]
  • ©1988
Description
1 online resource (VIII, 172 p.)

Details

Subject(s)
Iterative methods (Mathematics) [Browse]
Editor
Series
  • Lecture notes in mathematics (Berlin) ; Volume 1347. [More in this series]
  • Lecture Notes in Mathematics ; Volume 1347
Summary note
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.
Notes
Bibliographic Level Mode of Issuance: Monograph
Source of description
Description based on print version record.
Language note
English
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.
ISBN
3-540-45971-5
OCLC
  • 1066199580
  • 1113036843
Doi
  • 10.1007/BFb0079769
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