F 

(x)=4µ x(1x), µÎ[ 0,1) 
To each xÎ I is associated the infinite word a(x)Î{0,1}^{*} whose kth letter is 0 if F_{µ}^{k}(x)£1/2 and 1 otherwise. The aim of Cristopher Moore and Porus Lakdawala [6] is to study the language L formed by the set of prefixes of all a(x) for xÎ I (the symbolic dynamics of F_{µ}) and its evolution as µ increases from 0 to 1. For instance, the language corresponding to µ in Figure 2 is
L=0 

1 

(10) 

(1011) 

. 
L=0 

1 

(10) 

(1011) 

(10111010) 

. 
Figure 3: Limit cycle for µ=0.887.
Figure 4: Limit cycle for µ=0.89.
L_{0}(z)= 

, L_{n}(z)=L_{n1}(z) 

. 



This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.