Boundary of the Rauzy fractal sets in $\RR \times \CC$ generated by $P(x)=x^4-x^3-x^2-x-1$
| dc.creator | Durand, Fabien | |
| dc.creator | Messaoudi, Ali | |
| dc.date | 2008-07-21 | |
| dc.date | 2008-07-22 | |
| dc.date.accessioned | 2026-07-07T09:51:53Z | |
| dc.date.available | 2026-07-07T09:51:53Z | |
| dc.description | We study the boundary of the 3-dimensional Rauzy fractal ${\mathcal E} \subset \RR \times \CC$ generated by the polynomial $P(x) = x^4-x^3-x^2-x-1$. 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. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0807.3321 | |
| dc.identifier | http://arxiv.org/abs/0807.3321 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165399 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B85 | |
| dc.title | Boundary of the Rauzy fractal sets in $\RR \times \CC$ generated by $P(x)=x^4-x^3-x^2-x-1$ | |
| dc.type | text |