Geodesic
Connectedness of fractals associated with Arnoux-Rauzy substitutions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 249-266
Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux-Rauzy substitutions.

DOI : 10.1051/ita/2014008
Classification : 68R15, 37B10
Keywords: Rauzy fractals, Arnoux-Rauzy substitutions, discrete planes 
@article{ITA_2014__48_3_249_0,
     author = {Berth\'e, Val\'erie and Jolivet, Timo and Siegel, Anne},
     title = {Connectedness of fractals associated with {Arnoux-Rauzy} substitutions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {249--266},
     year = {2014},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     doi = {10.1051/ita/2014008},
     mrnumber = {3302487},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014008/}
}
TY  - JOUR
AU  - Berthé, Valérie
AU  - Jolivet, Timo
AU  - Siegel, Anne
TI  - Connectedness of fractals associated with Arnoux-Rauzy substitutions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2014
SP  - 249
EP  - 266
VL  - 48
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ita/2014008/
DO  - 10.1051/ita/2014008
LA  - en
ID  - ITA_2014__48_3_249_0
ER  - 
%0 Journal Article
%A Berthé, Valérie
%A Jolivet, Timo
%A Siegel, Anne
%T Connectedness of fractals associated with Arnoux-Rauzy substitutions
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2014
%P 249-266
%V 48
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ita/2014008/
%R 10.1051/ita/2014008
%G en
%F ITA_2014__48_3_249_0
Berthé, Valérie; Jolivet, Timo; Siegel, Anne. Connectedness of fractals associated with Arnoux-Rauzy substitutions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 249-266. doi: 10.1051/ita/2014008

Cité par Sources :