Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. (English) Zbl 07774923 J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997-5057 (2023). MSC: 37B10 37A30 37A44 11J70 11K50 11A55 11Y65 28A80 PDFBibTeX XMLCite \textit{V. Berthé} et al., J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997--5057 (2023; Zbl 07774923) Full Text: DOI arXiv
Berthé, Valérie; Cesaratto, Eda; Rotondo, Pablo; Safe, Martín D. Lochs-type theorems beyond positive entropy. (English) Zbl 07673373 Monatsh. Math. 200, No. 4, 737-779 (2023). Reviewer: Simon Kristensen (Aarhus) MSC: 11K55 11K50 11B57 28D20 PDFBibTeX XMLCite \textit{V. Berthé} et al., Monatsh. Math. 200, No. 4, 737--779 (2023; Zbl 07673373) Full Text: DOI arXiv
Berthé, Valérie; Cecchi Bernales, P.; Durand, Fabien; Leroy, Julien; Perrin, Dominique; Petite, S. On the dimension group of unimodular \(\mathcal{S}\)-adic subshifts. (English) Zbl 1469.37012 Monatsh. Math. 194, No. 4, 687-717 (2021). Reviewer: Bruno Duchesne (Nancy) MSC: 37B51 37B10 37A20 PDFBibTeX XMLCite \textit{V. Berthé} et al., Monatsh. Math. 194, No. 4, 687--717 (2021; Zbl 1469.37012) Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. On the second Lyapunov exponent of some multidimensional continued fraction algorithms. (English) Zbl 1473.11012 Math. Comput. 90, No. 328, 883-905 (2021). Reviewer: Takao Komatsu (Hangzhou) MSC: 11A55 11J70 11K50 37D25 PDFBibTeX XMLCite \textit{V. Berthé} et al., Math. Comput. 90, No. 328, 883--905 (2021; Zbl 1473.11012) Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M.; Yassawi, Reem Recognizability for sequences of morphisms. (English) Zbl 1476.37022 Ergodic Theory Dyn. Syst. 39, No. 11, 2896-2931 (2019). MSC: 37B10 37B52 37B51 03D40 05A05 PDFBibTeX XMLCite \textit{V. Berthé} et al., Ergodic Theory Dyn. Syst. 39, No. 11, 2896--2931 (2019; Zbl 1476.37022) Full Text: DOI arXiv
Berthé, Valérie; Cecchi Bernales, Paulina Balancedness and coboundaries in symbolic systems. (English) Zbl 1423.68366 Theor. Comput. Sci. 777, 93-110 (2019). MSC: 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{P. Cecchi Bernales}, Theor. Comput. Sci. 777, 93--110 (2019; Zbl 1423.68366) Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Geometry, dynamics, and arithmetic of \(S\)-adic shifts. (Géométrie, dynamique, et arithmétique des décalages \(S\)-adiques.) (English. French summary) Zbl 1433.37010 Ann. Inst. Fourier 69, No. 3, 1347-1409 (2019). Reviewer: Thomas B. Ward (Leeds) MSC: 37B10 37B52 37A46 11K31 11K50 28A80 PDFBibTeX XMLCite \textit{V. Berthé} et al., Ann. Inst. Fourier 69, No. 3, 1347--1409 (2019; Zbl 1433.37010) Full Text: DOI arXiv
Berthé, Valérie; Rigo, Michel General framework. (English) Zbl 1407.11044 Berthé, Valérie (ed.) et al., Sequences, groups, and number theory. Cham: Birkhäuser. Trends Math., 1-36 (2018). MSC: 11B85 11-02 05A05 11A63 68Q45 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{M. Rigo}, in: Sequences, groups, and number theory. Cham: Birkhäuser. 1--36 (2018; Zbl 1407.11044) Full Text: DOI
Berthé, V.; Dolce, F.; Durand, F.; Leroy, J.; Perrin, D. Rigidity and substitutive dendric words. (English) Zbl 1448.68365 Int. J. Found. Comput. Sci. 29, No. 5, 705-720 (2018). Reviewer: Jean-Paul Allouche (Paris) MSC: 68R15 11B85 37B10 PDFBibTeX XMLCite \textit{V. Berthé} et al., Int. J. Found. Comput. Sci. 29, No. 5, 705--720 (2018; Zbl 1448.68365) Full Text: DOI
Berthé, Valérie; Lhote, Loïck; Vallée, Brigitte The Brun gcd algorithm in high dimensions is almost always subtractive. (English) Zbl 1427.11143 J. Symb. Comput. 85, 72-107 (2018). MSC: 11Y16 68W40 PDFBibTeX XMLCite \textit{V. Berthé} et al., J. Symb. Comput. 85, 72--107 (2018; Zbl 1427.11143) Full Text: DOI
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 PDFBibTeX XMLCite \textit{V. Berthé} et al., Ergodic Theory Dyn. Syst. 36, No. 6, 1757--1794 (2016; Zbl 1378.37036) Full Text: DOI arXiv
Berthé, Valérie; De Felice, Clelia; Dolce, Francesco; Leroy, Julien; Perrin, Dominique; Reutenauer, Christophe; Rindone, Giuseppina Maximal bifix decoding. (English) Zbl 1309.68159 Discrete Math. 338, No. 5, 725-742 (2015). Reviewer: Francine Blanchet-Sadri (Greensboro) MSC: 68R15 PDFBibTeX XMLCite \textit{V. Berthé} et al., Discrete Math. 338, No. 5, 725--742 (2015; Zbl 1309.68159) Full Text: DOI arXiv
Berthé, Valérie; Lacasse, Annie; Paquin, Geneviève; Provençal, Xavier A study of Jacobi-Perron boundary words for the generation of discrete planes. (English) Zbl 1296.68113 Theor. Comput. Sci. 502, 118-142 (2013). MSC: 68R15 52C35 PDFBibTeX XMLCite \textit{V. Berthé} et al., Theor. Comput. Sci. 502, 118--142 (2013; Zbl 1296.68113) Full Text: DOI
Berthé, Valérie; Cassaigne, Julien; Steiner, Wolfgang Balance properties of Arnoux-Rauzy words. (English) Zbl 1269.68073 Int. J. Algebra Comput. 23, No. 4, 689-703 (2013). MSC: 68R15 37B10 PDFBibTeX XMLCite \textit{V. Berthé} et al., Int. J. Algebra Comput. 23, No. 4, 689--703 (2013; Zbl 1269.68073) Full Text: DOI arXiv
Berthé, V. Numeration and discrete dynamical systems. (English) Zbl 1269.11009 Computing 94, No. 2-4, 369-387 (2012). Reviewer: Michel Rigo (Liège) MSC: 11A63 11J70 37B10 11K16 PDFBibTeX XMLCite \textit{V. Berthé}, Computing 94, No. 2--4, 369--387 (2012; Zbl 1269.11009) Full Text: DOI
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 PDFBibTeX XMLCite \textit{V. Berthé} et al., Adv. Math. 226, No. 1, 139--175 (2011; Zbl 1221.11018) Full Text: DOI arXiv
Berthé, Valérie Discrete geometry and numeration. (English) Zbl 1480.37022 Actes Rencontres C.I.R.M. 1, No. 1, 17-22 (2009). MSC: 37B10 37B51 37B52 37E15 11A55 52C99 PDFBibTeX XMLCite \textit{V. Berthé}, Actes Rencontres C.I.R.M. 1, No. 1, 17--22 (2009; Zbl 1480.37022) Full Text: DOI Link
Berthé, Valérie Arithmetic discrete planes are quasicrystals. (English) Zbl 1261.52013 Brlek, Srečko (ed.) et al., Discrete geometry for computer imagery. 15th IAPR international conference, DGCI 2009, Montréal, Canada, September 30 – October 2, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04396-3/pbk). Lecture Notes in Computer Science 5810, 1-12 (2009). MSC: 52C23 52C22 68R15 PDFBibTeX XMLCite \textit{V. Berthé}, Lect. Notes Comput. Sci. 5810, 1--12 (2009; Zbl 1261.52013) 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 PDFBibTeX XMLCite \textit{S. Akiyama} et al., Monatsh. Math. 155, No. 3--4, 377--419 (2008; Zbl 1190.11005) Full Text: DOI arXiv
Berthé, Valerie; Siegel, Anne Purely periodic \(\beta \)-expansions in the Pisot non-unit case. (English) Zbl 1197.11139 J. Number Theory 127, No. 2, 153-172 (2007). MSC: 11R06 37B10 11A63 11J70 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{A. Siegel}, J. Number Theory 127, No. 2, 153--172 (2007; Zbl 1197.11139) Full Text: DOI arXiv
Arnoux, Pierre; Berthé, Valérie; Fernique, Thomas; Jamet, Damien Functional stepped surfaces, flips, and generalized substitutions. (English) Zbl 1119.68136 Theor. Comput. Sci. 380, No. 3, 251-265 (2007). MSC: 68R15 05C45 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Theor. Comput. Sci. 380, No. 3, 251--265 (2007; Zbl 1119.68136) Full Text: DOI Link
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne Fractal representation of the attractive lamination of an automorphism of the free group. (English) Zbl 1146.20020 Ann. Inst. Fourier 56, No. 7, 2161-2212 (2006). Reviewer: Dimitrios Varsos (Athenai) MSC: 20E05 37B10 20E36 05B45 68R15 57M07 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Ann. Inst. Fourier 56, No. 7, 2161--2212 (2006; Zbl 1146.20020) Full Text: DOI Numdam 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 PDFBibTeX XMLCite \textit{G. Barat} et al., Ann. Inst. Fourier 56, No. 7, 1987--2092 (2006; Zbl 1138.37005) Full Text: DOI Numdam EuDML
Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie Arithmetic distributions of convergents arising from Jacobi-Perron algorithm. (English) Zbl 1184.11024 Indag. Math., New Ser. 17, No. 2, 169-185 (2006). Reviewer: Simon Kristensen (Aarhus) MSC: 11K50 37A45 PDFBibTeX XMLCite \textit{V. Berthé} et al., Indag. Math., New Ser. 17, No. 2, 169--185 (2006; Zbl 1184.11024) Full Text: DOI
Arnoux, Pierre; Berthé, Valérie; Siegel, Anne Two-dimensional iterated morphisms and discrete planes. (English) Zbl 1068.37004 Theor. Comput. Sci. 319, No. 1-3, 145-176 (2004). MSC: 37B10 05A05 05B25 37B50 68R15 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Theor. Comput. Sci. 319, No. 1--3, 145--176 (2004; Zbl 1068.37004) Full Text: DOI
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. (English) Zbl 1017.11006 Ann. Inst. Fourier 52, No. 2, 305-349 (2002). Reviewer: Takao Komatsu (Tsu, Mie) MSC: 11A55 11J70 40A15 68R15 PDFBibTeX XMLCite \textit{P. Arnoux} et al., Ann. Inst. Fourier 52, No. 2, 305--349 (2002; Zbl 1017.11006) Full Text: DOI Numdam EuDML
Berthé, Valérie; Tijdeman, Robert Balance properties of multi-dimensional words. (English) Zbl 0997.68091 Theor. Comput. Sci. 273, No. 1-2, 197-224 (2002). MSC: 68R15 PDFBibTeX XMLCite \textit{V. Berthé} and \textit{R. Tijdeman}, Theor. Comput. Sci. 273, No. 1--2, 197--224 (2002; Zbl 0997.68091) Full Text: DOI