Shutov, A. V. Rauzy fractals and their number-theoretic applications. (English. Russian original) Zbl 1486.11092 J. Math. Sci., New York 260, No. 2, 265-274 (2022); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 166, 110-119 (2019). Reviewer: Mehdi Hassani (Zanjan) MSC: 11J71 11A63 11K38 28A80 × Cite Format Result Cite Review PDF Full Text: DOI
Scheicher, Klaus; Sirvent, Víctor F.; Surer, Paul Measure-wise disjoint Rauzy fractals with the same incidence matrix. (English) Zbl 1462.28011 Monatsh. Math. 194, No. 4, 857-871 (2021). Reviewer: Peter Massopust (München) MSC: 28A80 11B85 37B10 × Cite Format Result Cite Review PDF Full Text: DOI
Thuswaldner, Jörg M. \(S\)-adic sequences: a bridge between dynamics, arithmetic, and geometry. (English) Zbl 1457.37014 Akiyama, Shigeki (ed.) et al., Substitution and tiling dynamics: introduction to self-inducing structures. Lecture notes from the research school on tiling dynamical systems, CIRM Jean-Morlet Chair, Marseille, France, Fall 2017. Cham: Springer. Lect. Notes Math. 2273, 97-191 (2020). Reviewer: Alexei Kanel-Belov (Ramat-Gan) MSC: 37B10 37B52 37E15 52C22 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Surer, Paul Substitutive number systems. (English) Zbl 1473.11019 Int. J. Number Theory 16, No. 8, 1709-1751 (2020). Reviewer: Toufik Zaïmi (Riyadh) MSC: 11A63 37B10 68R15 11R06 × Cite Format Result Cite Review PDF Full Text: DOI
Mercat, Paul Rauzy fractal of the smallest substitution associated with the smallest Pisot number. (English) Zbl 1441.28010 Exp. Math. 29, No. 2, 163-182 (2020). MSC: 28A80 37B10 37F20 68R15 × Cite Format Result Cite Review PDF Full Text: DOI
Hejda, Tomáš Multiple tilings associated to \(d\)-Bonacci beta-expansions. (English) Zbl 1445.11005 Monatsh. Math. 187, No. 2, 275-291 (2018). MSC: 11A63 11R06 37B10 52C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Barge, Marcy The Pisot conjecture for \(\beta\)-substitutions. (English) Zbl 1457.37025 Ergodic Theory Dyn. Syst. 38, No. 2, 444-472 (2018). MSC: 37B52 37B10 37A44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Thuswaldner, Jörg M. Discrepancy bounds for \(\boldsymbol{\beta}\)-adic Halton sequences. (English) Zbl 1431.11098 Elsholtz, Christian (ed.) et al., Number theory – Diophantine problems, uniform distribution and applications. Festschrift in honour of Robert F. Tichy’s 60th birthday. Cham: Springer. 423-444 (2017). MSC: 11K38 11A63 11J87 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sellami, Tarek; Sirvent, Víctor F. Symmetric intersections of Rauzy fractals. (English) Zbl 1423.28027 Quaest. Math. 39, No. 3, 289-305 (2016). MSC: 28A80 11B85 37B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, Valérie; Bourdon, Jérémie; Jolivet, Timo; Siegel, Anne A combinatorial approach to products of Pisot substitutions. (English) Zbl 1378.37036 Ergodic Theory Dyn. Syst. 36, No. 6, 1757-1794 (2016). MSC: 37B50 37B10 28A80 37A45 11K16 52C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Steiner, Wolfgang; Thuswaldner, Jörg M. Rational self-affine tiles. (English) Zbl 1329.52019 Trans. Am. Math. Soc. 367, No. 11, 7863-7894 (2015). Reviewer: Judit Abardia (Frankfurt a. M.) MSC: 52C22 11A63 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bastos, J.; Messaoudi, A.; Rodrigues, T.; Smania, D. A class of cubic Rauzy fractals. (English) Zbl 1332.28012 Theor. Comput. Sci. 588, 114-130 (2015). Reviewer: Peter Massopust (München) MSC: 28A80 11A63 68Q45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Minervino, Milton; Thuswaldner, Jörg The geometry of non-unit Pisot substitutions. (Géométrie des substitutions de type Pisot non unimodulaires.) (English. French summary) Zbl 1309.05045 Ann. Inst. Fourier 64, No. 4, 1373-1417 (2014). Reviewer: Thomas B. Ward (Durham) MSC: 05B45 11A63 11F85 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bruin, Henk; Kalle, Charlene Natural extensions for piecewise affine maps via Hofbauer towers. (English) Zbl 1306.37005 Monatsh. Math. 175, No. 1, 65-88 (2014). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 37A05 37B10 28A75 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Minervino, Milton; Steiner, Wolfgang Tilings for Pisot beta numeration. (English) Zbl 1293.11084 Indag. Math., New Ser. 25, No. 4, 745-773 (2014). MSC: 11K16 11K55 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rao, Hui; Wen, Zhi-Ying; Yang, Ya-Min Dual systems of algebraic iterated function systems. (English) Zbl 1294.28011 Adv. Math. 253, 63-85 (2014). Reviewer: Boris A. Kats (Kazan) MSC: 28A80 × Cite Format Result Cite Review PDF Full Text: DOI
Kalle, Charlene; Steiner, Wolfgang Beta-expansions, natural extensions and multiple tilings associated with Pisot units. (English) Zbl 1295.11010 Trans. Am. Math. Soc. 364, No. 5, 2281-2318 (2012). Reviewer: Manfred G. Madritsch (Vandœuvre) MSC: 11A67 11R06 28A80 28D05 37B10 52C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Durand, Fabien; Messaoudi, Ali Boundary of the Rauzy fractal sets in \(\mathbb {R} \times \mathbb {C}\) generated by \(P(x) = x^4 - x^3 - x^2 - x - 1\). (English) Zbl 1268.11039 Osaka J. Math. 48, No. 2, 471-496 (2011). MSC: 11B85 11K16 28A80 52C22 × Cite Format Result Cite Review PDF Full Text: arXiv Euclid
Akiyama, Shigeki; Lee, Jeong-Yup Algorithm for determining pure pointedness of self-affine tilings. (English) Zbl 1219.37013 Adv. Math. 226, No. 4, 2855-2883 (2011). Reviewer: Nicolae-Adrian Secelean (Sibiu) MSC: 37B50 28A80 52C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M. Fractal tiles associated with shift radix systems. (English) Zbl 1221.11018 Adv. Math. 226, No. 1, 139-175 (2011). Reviewer: Elizaveta Zamorzaeva (Chişinău) MSC: 11A63 28A80 52C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Akiyama, Shigeki Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems. (English) Zbl 1474.11022 Actes Rencontres C.I.R.M. 1, No. 1, 3-9 (2009). MSC: 11A63 37B10 × Cite Format Result Cite Review PDF Full Text: DOI
Akiyama, Shigeki; Barat, Guy; Berthé, Valérie; Siegel, Anne Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. (English) Zbl 1190.11005 Monatsh. Math. 155, No. 3-4, 377-419 (2008). Reviewer: Takao Komatsu (Hirosaki) MSC: 11A63 03D45 11S99 28A75 52C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sing, B.; Sirvent, V. F. Geometry of the common dynamics of flipped Pisot substitutions. (English) Zbl 1190.11016 Monatsh. Math. 155, No. 3-4, 431-448 (2008). Reviewer: Francine Blanchet-Sadri (Greensboro) MSC: 11B85 28A80 37B10 68Q45 68R15 × Cite Format Result Cite Review PDF Full Text: DOI
Lee, Jeong-Yup Substitution Delone sets with pure point spectrum are inter-model sets. (English) Zbl 1132.52022 J. Geom. Phys. 57, No. 11, 2263-2285 (2007). MSC: 52C23 37B50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Hao; Luo, Jun; Yin, JianDong The properties of a family of tiles with a parameter. (English) Zbl 1125.37008 J. Math. Anal. Appl. 335, No. 2, 1383-1396 (2007). Reviewer: Yuang-Ling Ye (Guangzhou) MSC: 37B50 28A80 52C20 × Cite Format Result Cite Review PDF Full Text: DOI
Ito, Shunji; Rao, H. Atomic surfaces, tilings and coincidence. I: Irreducible case. (English) Zbl 1143.37013 Isr. J. Math. 153, 129-155 (2006). Reviewer: Elizaveta Zamorzaeva (Chişinău) MSC: 37B50 52C22 × Cite Format Result Cite Review PDF Full Text: DOI
Ei, Hiromi; Ito, Shunji; Rao, Hui Atomic surfaces, tilings and coincidences. II: Reducible case. (English) Zbl 1119.52013 Ann. Inst. Fourier 56, No. 7, 2285-2313 (2006). MSC: 52C23 37A45 28A80 11B85 × Cite Format Result Cite Review PDF Full Text: DOI Numdam Numdam EuDML
Baker, Veronica; Barge, Marcy; Kwapisz, Jaroslaw Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to \(\beta\)-shifts. (English) Zbl 1138.37008 Ann. Inst. Fourier 56, No. 7, 2213-2248 (2006). MSC: 37B50 11R06 37A45 28D05 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Barat, Guy; Berthé, Valérie; Liardet, Pierre; Thuswaldner, Jörg Dynamical directions in numeration. (English) Zbl 1138.37005 Ann. Inst. Fourier 56, No. 7, 1987-2092 (2006). Reviewer: Olaf Ninnemann (Berlin) MSC: 37B10 11A63 11J70 37A45 68Q45 68R15 37-02 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Thuswaldner, Jörg M. Unimodular Pisot substitutions and their associated tiles. (English) Zbl 1161.37016 J. Théor. Nombres Bordx. 18, No. 2, 487-536 (2006). Reviewer: Takao Komatsu (Hirosaki) MSC: 37B10 11B85 11K55 28A80 52C22 × Cite Format Result Cite Review PDF Full Text: DOI Numdam Numdam EuDML
Akiyama, Shigeki; Thuswaldner, J. M. The topological structure of fractal tilings generated by quadratic number systems. (English) Zbl 1123.11004 Comput. Math. Appl. 49, No. 9-10, 1439-1485 (2005). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11A63 11K55 28A80 37B50 05B45 52C22 × Cite Format Result Cite Review PDF Full Text: DOI
Zhuravlev, V. G. Rauzy tilings and bounded remainder sets on the torus. (English, Russian) Zbl 1158.11331 J. Math. Sci., New York 137, No. 2, 4658-4672 (2006); translation from Zap. Nauchn. Semin. POMI 322, 83-106 (2005). MSC: 11K99 11J71 37B99 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Ito, Shunji; Rao, Hui Purely periodic \(\beta\)-expansions with Pisot unit base. (English) Zbl 1099.11062 Proc. Am. Math. Soc. 133, No. 4, 953-964 (2005). Reviewer: Artūras Dubickas (Vilnius) MSC: 11R06 37B50 11K16 × Cite Format Result Cite Review PDF Full Text: DOI
Akiyama, Shigeki; Thuswaldner, Jörg M. A survey on topological properties of tiles related to number systems. (English) Zbl 1073.37017 Geom. Dedicata 109, 89-105 (2004). MSC: 37B50 11A63 54D05 11K55 28A80 37A45 × Cite Format Result Cite Review PDF Full Text: DOI
Akiyama, Shigeki; Rao, Hui; Steiner, Wolfgang A certain finiteness property of Pisot number systems. (English) Zbl 1052.11055 J. Number Theory 107, No. 1, 135-160 (2004). Reviewer: Jean-Paul Allouche (Orsay) MSC: 11K16 11A63 11R06 37A45 37B10 × Cite Format Result Cite Review PDF Full Text: DOI