Boundary of the rauzy fractal sets in ℝ×ℂgenerated by p(x) = x 4- x 3 - x 2 -x- 1
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2011-06-01
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Durand, Fabien
Messaoudi, Ali [UNESP]
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We study the boundary of the 3-dimensional Rauzy fractal ε ⊂ ℝ×ℂ generated by the polynomial P(x) Dx 4-x 3-x 2-x-1. The finite automaton characterizing the boundary of ε is given explicitly. As a consequence we prove that the set ε has 18 neighboors where 6 of them intersect the central tile ε 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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Osaka Journal of Mathematics, v. 48, n. 2, p. 471-496, 2011.