Geodesic
Dividing toric tilings and bounded remainder sets
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 99-122 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

An infinite sequence of dividing two-dimensional toric tilings is constructed by using differentiation of toric developments admitting a rearrangement. We prove that the nucleus of these tilings is a bounded remainder set. 
@article{ZNSL_2015_440_a7,
     author = {V. G. Zhuravlev},
     title = {Dividing toric tilings and bounded remainder sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--122},
     year = {2015},
     volume = {440},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/}
}
TY  - JOUR
AU  - V. G. Zhuravlev
TI  - Dividing toric tilings and bounded remainder sets
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 99
EP  - 122
VL  - 440
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/
LA  - ru
ID  - ZNSL_2015_440_a7
ER  - 
%0 Journal Article
%A V. G. Zhuravlev
%T Dividing toric tilings and bounded remainder sets
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 99-122
%V 440
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/
%G ru
%F ZNSL_2015_440_a7
V. G. Zhuravlev. Dividing toric tilings and bounded remainder sets. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 99-122. http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a7/

[1] V. G. Zhuravlev, “Indutsirovannye mnozhestva ogranichennogo ostatka”, Algebra i analiz (to appear)

[2] V. G. Zhuravlev, “Razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Zap. nauchn. semin. POMI, 322, 2005, 83–106 | MR | Zbl

[3] A. V. Shutov, A. V. Maleev, V. G. Zhuravlev, “Complex quasiperiodic self-similar tilings: their parameterization, boundaries, complexity, growth and symmetry”, Acta Crystallogr., A66 (2010), 427–437 | DOI | MR

[4] G. Rauzy, “Ensembles à restes bornés”, Seminar on number theory, 1983–1984 (Talence, 1983/1984), Univ. Bordeaux, Talence, 1984, Exposé No. 24, 12 pp. | MR

[5] S. Ferenczi, “Bounded Remaider Sets”, Acta Arith., 61:4 (1992), 319–326 | MR | Zbl

[6] E. Hecke, “Über analytische Funktionen und die Verteilung von Zahlen mod Eins”, Math. Semin. Hamburg. Univ., 1 (1921), 54–76 | DOI | MR

[7] V. G. Zhuravlev, “Odnomernye razbieniya Fibonachchi”, Izv. RAN. Ser. mat., 71:2 (2007), 287–321 | MR

[8] M. Morse, C. A. Hedlund, “Symbolic Dynamics. II: Sturmian trajectories”, Amer. J. Math., 62 (1940), 1–42 | DOI | MR

[9] H. Weyl, “Über die Gleichverteilung von Zahlen $\mathrm{mod}$ Eins”, Math. Ann., 77 (1916), 313–352 | DOI | MR | Zbl