Boundary of the Rauzy fractal sets in \RR × \CC generated by P(x)=x⁴-x³-x²-x-1

2008/07/21 by Fabien Durand, Durand, Fabien, Ali Messaoudi +1
Mathematics · #11B85 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11B85

paper · pdf · doi:10.48550/arxiv.0807.3321

19 pages

arxiv created 2008/07/22 · arxiv updated 2009/12/01

Abstract

We study the boundary of the 3-dimensional Rauzy fractal \mathcal E ⊂ \RR × \CC generated by the polynomial P(x) = x⁴-x³-x²-x-1. The finite automaton characterizing the boundary of \mathcal E is given explicitly. As a consequence we prove that the set \mathcal E has 18 neighborhoods where 6 of them intersect the central tile \mathcal E in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.

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