Geodesic
Rauzy fractals and their number-theoretic applications
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 110-119

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we construct and study Rauzy partitions of order $n$ for a certain class of Pisot numbers. These partitions are partitions of a torus into fractal sets. Moreover, the action of a certain shift of the torus on partitions introduced is reduced to rearranging the partition tiles. We obtain a number of applications of partitions introduced to the study of the corresponding shift of the torus. In particular, we prove that partition tiles are bounded-remainder sets with respect to the shift considered. In addition, we obtain a number of applications to the study of sets of positive integers that have a given ending of the greedy expansion by a linear recurrent sequence and to generalized Knuth–Matiyasevich multiplications.
Mots-clés : Rauzy partition
Keywords: numeral system, bounded remainder set, additive problem. 
@article{INTO_2019_166_a10,
     author = {A. V. Shutov},
     title = {Rauzy fractals and their number-theoretic applications},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {110--119},
     publisher = {mathdoc},
     volume = {166},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_166_a10/}
}
TY  - JOUR
AU  - A. V. Shutov
TI  - Rauzy fractals and their number-theoretic applications
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 110
EP  - 119
VL  - 166
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_166_a10/
LA  - ru
ID  - INTO_2019_166_a10
ER  - 
%0 Journal Article
%A A. V. Shutov
%T Rauzy fractals and their number-theoretic applications
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 110-119
%V 166
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_166_a10/
%G ru
%F INTO_2019_166_a10
A. V. Shutov. Rauzy fractals and their number-theoretic applications. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 110-119. http://geodesic.mathdoc.fr/item/INTO_2019_166_a10/