Berthé, V.; Dajani, K.; Kalle, C.; Krawczyk, E.; Kuru, H.; Thevis, A. Rational approximations, multidimensional continued fractions, and lattice reduction. (English) Zbl 07919514 Abdellatif, Ramla (ed.) et al., Women in numbers Europe IV. Research directions in number theory. Selected papers based on the presentations at the 4th workshop, WINE 4, Utrecht, the Netherlands, August 29 – September 2, 2022. Cham: Springer. Assoc. Women Math. Ser. 32, 111-154 (2024). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 11K50 11K55 11A55 11Y16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cheung, Yitwah; Chevallier, Nicolas Lévy-Khintchin theorem for best simultaneous Diophantine approximations. (Théorème de Lévy-Khintchin pour les meilleures approximations diophantiennes simultanées.) (English. French summary) Zbl 07837750 Ann. Sci. Éc. Norm. Supér. (4) 57, No. 1, 185-240 (2024). Reviewer: Enrico Zoli (Faenza) MSC: 11J13 11J83 11K55 37A17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. (English) Zbl 1533.37040 J. Eur. Math. Soc. (JEMS) 25, No. 12, 4997-5057 (2023). MSC: 37B10 37A30 37A44 11J70 11K50 11A55 11Y65 28A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chevallier, Nicolas The natural extension of the Gauss map and the Hermite best approximations. (English. French summary) Zbl 1508.11073 J. Théor. Nombres Bordx. 34, No. 2, 619-636 (2022). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J70 37A44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Andersen, Nickolas; Duke, William The Minkowski chain and Diophantine approximation. (English. French summary) Zbl 1460.11098 J. Théor. Nombres Bordx. 32, No. 2, 503-523 (2020). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11J13 11J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hockman, Meira The Farey octahedron graph, the Poincaré polyhedron theorem and Gaussian integer continued fractions. (English. French summary) Zbl 1437.05196 Ann. Math. Qué. 44, No. 1, 149-164 (2020). MSC: 05C70 05B45 52C22 20G20 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Lopes Dias, João; Gaivão, José Pedro Linearization of Gevrey flows on \(\mathbb{T}^d\) with a Brjuno type arithmetical condition. (English) Zbl 1441.37066 J. Differ. Equations 267, No. 12, 7167-7212 (2019). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 37J40 37C10 37C55 11J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vodička, Martin; Zlatoš, Pavol Ján A uniform stability principle for dual lattices. (English) Zbl 1446.11131 J. Log. Anal. 11, Paper No. 2, 22 p. (2019). MSC: 11H06 11H31 11H60 03H05 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Mundici, Daniele Triangles in Diophantine approximation. (English) Zbl 1459.11018 J. Number Theory 201, 176-189 (2019). MSC: 11A55 11B57 11Y65 11J70 11K60 14M25 22F05 37A20 37C85 40A15 × Cite Format Result Cite Review PDF Full Text: DOI
Hockman, Meira The geometry of Gaussian integer continued fractions. (English) Zbl 1405.52021 J. Number Theory 197, 145-167 (2019). MSC: 52C22 20G20 51M10 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Bekki, Hohto On periodicity of geodesic continued fractions. (English) Zbl 1428.11127 J. Number Theory 177, 181-210 (2017). MSC: 11J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jonckheere, E.; Langbein, F. C.; Schirmer, S. G. Information transfer fidelity in spin networks and ring-based quantum routers. (English) Zbl 1333.81077 Quantum Inf. Process. 14, No. 12, 4751-4785 (2015). MSC: 81P45 94A40 81Q37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Drouin, Christian A two-dimensional continued fraction algorithm with Lagrange and Dirichlet properties. (English. French summary) Zbl 1370.11084 J. Théor. Nombres Bordx. 26, No. 2, 307-346 (2014). MSC: 11J70 11J13 11Y16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Numdam
Beukers, Frits Geodesic continued fractions and LLL. (English) Zbl 1369.11050 Indag. Math., New Ser. 25, No. 4, 632-645 (2014). MSC: 11J70 11J13 11Y65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fox, Adam M.; Meiss, James D. Greene’s residue criterion for the breakup of invariant tori of volume-preserving maps. (English) Zbl 1259.37036 Physica D 243, No. 1, 45-63 (2013). MSC: 37J40 34C27 70H08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bonckaert, P.; Verstringe, F. Renormalization of planar analytic saddles. (English) Zbl 1256.34027 J. Dyn. Differ. Equations 24, No. 3, 569-593 (2012). Reviewer: Eugene Ershov (St. Petersburg) MSC: 34C20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Lopes Dias, João KAM theory as a limit of renormalization. (English) Zbl 1253.37059 Peixoto, Maurício Matos (ed.) et al., Dynamics, games and science I. DYNA 2008, in honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8–12, 2008. Papers based on talks given at the international conference. Berlin: Springer (ISBN 978-3-642-11455-7/hbk; 978-3-642-11456-4/ebook). Springer Proceedings in Mathematics 1, 253-270 (2011). MSC: 37J40 37E20 × Cite Format Result Cite Review PDF Full Text: DOI
Berthé, Valérie; Fernique, Thomas Brun expansions of stepped surfaces. (English) Zbl 1236.11011 Discrete Math. 311, No. 7, 521-543 (2011). Reviewer: Wolfgang Steiner (Sydney) MSC: 11A55 52B99 68R15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Koch, Hans; Kocić, Saša A renormalization approach to lower-dimensional tori with Brjuno frequency vectors. (English) Zbl 1214.37043 J. Differ. Equations 249, No. 8, 1986-2004 (2010). Reviewer: Yuri V. Rogovchenko (Umeå) MSC: 37J40 37J35 × Cite Format Result Cite Review PDF Full Text: DOI
Koch, Hans; Kocić, Saša A renormalization group approach to quasiperiodic motion with Brjuno frequencies. (English) Zbl 1201.34003 Ergodic Theory Dyn. Syst. 30, No. 4, 1131-1146 (2010). Reviewer: Sergei Yu. Pilyugin (St. Petersburg) MSC: 34-02 34C20 37E20 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
Koch, Hans; Kocić, Saša Renormalization of vector fields and Diophantine invariant tori. (English) Zbl 1170.37015 Ergodic Theory Dyn. Syst. 28, No. 5, 1559-1585 (2008). Reviewer: Peter Zabreiko (Minsk) MSC: 37C27 37C10 37C55 37E25 37E45 37J40 × Cite Format Result Cite Review PDF Full Text: DOI
Dias, João Lopes Local conjugacy classes for analytic torus flows. (English) Zbl 1151.37026 J. Differ. Equations 245, No. 2, 468-489 (2008). Reviewer: Juan Campos (Granada) MSC: 37C55 37C15 37E10 37E45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tourigny, Yves; Smart, Nigel P. A multidimensional continued fraction based on a high-order recurrence relation. (English) Zbl 1201.11072 Math. Comput. 76, No. 260, 1995-2022 (2007). MSC: 11J13 11J70 × Cite Format Result Cite Review PDF Full Text: DOI
Khanin, Kostya; Lopes Dias, João; Marklof, Jens Multidimensional continued fractions, dynamical renormalization and KAM theory. (English) Zbl 1114.37009 Commun. Math. Phys. 270, No. 1, 197-231 (2007). MSC: 37A45 11J70 22F30 37E20 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chevallier, Nicolas Best simultaneous Diophantine approximations and Lévy’s theorem. (Meilleures approximations diophantiennes simultanées et théorème de Lévy.) (French) Zbl 1080.11052 Ann. Inst. Fourier 55, No. 5, 1635-1657 (2005). Reviewer: Robert F. Tichy (Graz) MSC: 11J13 11J70 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Beaver, Olga R.; Garrity, Thomas A two-dimensional Minkowski \(?(x)\) function. (English) Zbl 1064.11051 J. Number Theory 107, No. 1, 105-134 (2004). Reviewer: Takao Komatsu (Hirosaki) MSC: 11J70 11J68 11K60 26B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nogueira, Arnaldo The Borel-Bernstein theorem for multidimensional continued fractions. (English) Zbl 1015.11039 J. Anal. Math. 85, 1-41 (2001). Reviewer: L.Heinrich (Augsburg) MSC: 11K50 11K55 60F15 37B99 × Cite Format Result Cite Review PDF Full Text: DOI
Langtry, Timothy N. A construction of higher-rank lattice rules. (English) Zbl 0981.65005 Math. Comput. Simul. 55, No. 1-3, 103-111 (2001). Reviewer: D.Acu (Sibiu) MSC: 65C05 11J13 × Cite Format Result Cite Review PDF Full Text: DOI Link
Broise-Alamichel, Anne; Guivarc’h, Yves Exposants caractéristiques de l’algorithme de Jacobi-Perron et de la transformation associée. (Characteristic exponents of the Jacobi-Perron algorithm and of the associated map). (French) Zbl 1012.11060 Ann. Inst. Fourier 51, No. 3, 565-686 (2001). Reviewer: Valérie Berthé (Marseille) MSC: 11J70 11K50 37H15 11J13 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Chevallier, Nicolas Geometry of the Kronecker sequence. (Geométrie des suites de Kronecker.) (French) Zbl 0893.11028 Manuscr. Math. 94, No. 2, 231-241 (1997). Reviewer: R.F.Tichy (Graz) MSC: 11K06 52B99 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Grabiner, David J. Farey nets and multidimensional continued fractions. (English) Zbl 0765.11029 Monatsh. Math. 114, No. 1, 35-61 (1992). Reviewer: D.J.Grabiner (Cambridge/MA) MSC: 11J70 11J13 11J72 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Baldwin, P. R. A multidimensional continued fraction and some of its statistical properties. (English) Zbl 0891.11039 J. Stat. Phys. 66, No. 5-6, 1463-1505 (1992). MSC: 11K50 28D20 11J17 11Y16 37A99 × Cite Format Result Cite Review PDF Full Text: DOI