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Critical itineraries of maps with constant slope and one discontinuity

Published online by Cambridge University Press:  24 November 2014

MICHAEL BARNSLEY ,
WOLFGANG STEINER  and
ANDREW VINCE
MICHAEL BARNSLEY
Affiliation:
The Australian National University, Canberra, Australia. e-mail: michael.barnsley@anu.edu.au
WOLFGANG STEINER
Affiliation:
LIAFA, CNRS UMR 7089, Université Paris Diderot – Paris 7, Paris, France. e-mail: steiner@liafa.univ-paris-diderot.fr
ANDREW VINCE
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL, U.S.A. e-mail: avince@ufl.edu
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Abstract

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 3 , November 2014 , pp. 547 - 565
Copyright
Copyright © Cambridge Philosophical Society 2014 

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