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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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A set of binary sequences, unimodal functions, beta-expansions and Diophantine approximation
by
Jean-Paul Allouche
CNRS, LRI, Orsay

We describe a set of binary sequences studied by M. Cosnard and the author in 1982-1983 in the framework of iterations of continuous unimodal functions of the unit interval. This set happens to occur both in beta-expansions for "univoque´´ real numbers (i.e., real numbers in (1, 2) for which 1 has a unique beta-expansion) and in Diophantine approximation (the so-called Cassaigne spectrum also studied by Bugeaud and Laurent).

Date received: May 5, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-40.