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Noninteger bases, iteration of continuous real maps, and an arithmetic selfsimilar set
 

Summary: Non­integer bases, iteration of continuous real maps,
and an arithmetic self­similar set
J.­P. Allouche
CNRS, LRI, B“atiment 490
F­91405 Orsay Cedex
(France)
allouche@lri.fr
M. Cosnard
LORIA, 615 rue du Jardin Botanique
F­54602 Villers­l`es­Nancy Cedex
(France)
cosnard@loria.fr
1 Introduction
In a recent paper [29, Theorem 1, Lemma 1, and Theorem 3], Komornik and Loreti prove
the following results.
Theorem 1 ([29]) There exists a smallest q 2 (1; 2), for which there exists a unique ex­
pansion of 1 as 1 =
P 1
n=1
ffi n q \Gamman , with ffi n 2 f0; 1g. Furthermore, for this smallest q, the

  

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

 

Collections: Computer Technologies and Information Sciences