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The Quarterly Journal of Mathematics Advance Access published online on February 15, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham046
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© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

CLASSIFICATION OF A CLASS OF CONTINUOUS MAPS ON THE UNIT INTERVAL

D. J. Sawyer and J. K. Truss{dagger}

Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT

{dagger} Corresponding author. E-mail: pmtjkt{at}leeds.ac.uk

Received 20 December 2005; revised 9 August 2007
  Abstract

We give a classification of certain continuous maps from the unit interval (or any non-trivial closed bounded interval of the real line) to itself up to conjugacy. The maps studied are those for which there is a partition of the interval into finitely many subintervals whose endpoints form a cycle of the map, and on each of which the map is monotonic.


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