Bonanno, Claudio; Isola, Stefano Series expansions for Maass forms on the full modular group from the Farey transfer operators. (English) Zbl 07161177 J. Number Theory 210, 183-230 (2020). MSC: 11F37 11F72 37C30 PDF BibTeX XML Cite \textit{C. Bonanno} and \textit{S. Isola}, J. Number Theory 210, 183--230 (2020; Zbl 07161177) Full Text: DOI
Shi, Yong-Guo A note on the conjugacy from Farey map to the skew tent map. (English) Zbl 1414.37010 Bull. Malays. Math. Sci. Soc. (2) 42, No. 2, 649-656 (2019). MSC: 37C15 33E30 37B10 PDF BibTeX XML Cite \textit{Y.-G. Shi}, Bull. Malays. Math. Sci. Soc. (2) 42, No. 2, 649--656 (2019; Zbl 1414.37010) Full Text: DOI
Bonanno, Claudio; Giulietti, Paolo; Lenci, Marco Infinite mixing for one-dimensional maps with an indifferent fixed point. (English) Zbl 1404.37041 Nonlinearity 31, No. 11, 5180-5213 (2018). MSC: 37E05 37A40 37A25 37D25 37C25 PDF BibTeX XML Cite \textit{C. Bonanno} et al., Nonlinearity 31, No. 11, 5180--5213 (2018; Zbl 1404.37041) Full Text: DOI
Boca, Florin P.; Linden, Christopher On Minkowski type question mark functions associated with even or odd continued fractions. (English) Zbl 06936068 Monatsh. Math. 187, No. 1, 35-57 (2018). MSC: 11A25 26A30 11A55 11B57 11B83 37B10 37E25 PDF BibTeX XML Cite \textit{F. P. Boca} and \textit{C. Linden}, Monatsh. Math. 187, No. 1, 35--57 (2018; Zbl 06936068) Full Text: DOI
Boca, Florin P. The distribution of rational numbers and ergodic theory. (English) Zbl 1449.37001 Rev. Roum. Math. Pures Appl. 62, No. 1, 41-62 (2017). MSC: 37A05 37A44 37A17 PDF BibTeX XML Cite \textit{F. P. Boca}, Rev. Roum. Math. Pures Appl. 62, No. 1, 41--62 (2017; Zbl 1449.37001)
Granados, Albert; Alsedà, Lluís; Krupa, Maciej The period adding and incrementing bifurcations: from rotation theory to applications. (English) Zbl 1366.37097 SIAM Rev. 59, No. 2, 225-292 (2017). MSC: 37E10 37E05 37G15 37N25 37N35 PDF BibTeX XML Cite \textit{A. Granados} et al., SIAM Rev. 59, No. 2, 225--292 (2017; Zbl 1366.37097) Full Text: DOI
Du, Zhengdong Period-adding and the Farey tree structure in a class of one-dimensional discontinuous nonlinear maps. (English) Zbl 1355.37060 Nonlinear Dyn. 84, No. 4, 2211-2226 (2016). MSC: 37E05 37G10 37C25 PDF BibTeX XML Cite \textit{Z. Du}, Nonlinear Dyn. 84, No. 4, 2211--2226 (2016; Zbl 1355.37060) Full Text: DOI
Kesseböhmer, Marc; Munday, Sara; Stratmann, Bernd Otto Infinite ergodic theory of numbers. (English) Zbl 1362.37003 De Gruyter Graduate. Berlin: De Gruyter (ISBN 978-3-11-043941-0/pbk; 978-3-11-043942-7/ebook). xvi, 191 p. (2016). Reviewer: Christoph Aistleitner (Graz) MSC: 37-02 11-02 37A45 11J70 11K50 11K55 PDF BibTeX XML Cite \textit{M. Kesseböhmer} et al., Infinite ergodic theory of numbers. Berlin: De Gruyter (2016; Zbl 1362.37003) Full Text: DOI
Heersink, Byron An effective estimate for the Lebesgue measure of preimages of iterates of the Farey map. (English) Zbl 1362.37018 Adv. Math. 291, 621-634 (2016). Reviewer: Christoph Aistleitner (Graz) MSC: 37A40 37A45 11A55 11J70 PDF BibTeX XML Cite \textit{B. Heersink}, Adv. Math. 291, 621--634 (2016; Zbl 1362.37018) Full Text: DOI arXiv
Ben Ammou, S.; Bonanno, C.; Chouari, I.; Isola, S. On the leading eigenvalue of transfer operators of the Farey map with real temperature. (English) Zbl 1352.37111 Chaos Solitons Fractals 71, 60-65 (2015). MSC: 37E05 37C30 47A10 PDF BibTeX XML Cite \textit{S. Ben Ammou} et al., Chaos Solitons Fractals 71, 60--65 (2015; Zbl 1352.37111) Full Text: DOI arXiv
Odegard, Issac; Zerr, Ryan J. The quadratic irrationals and Ducci matrix sequences. (English) Zbl 1381.11008 Linear Algebra Appl. 484, 344-355 (2015). MSC: 11A55 11B57 15A99 39B42 PDF BibTeX XML Cite \textit{I. Odegard} and \textit{R. J. Zerr}, Linear Algebra Appl. 484, 344--355 (2015; Zbl 1381.11008) Full Text: DOI
Böhm, Janko; Decker, Wolfram; Fieker, Claus; Pfister, Gerhard The use of bad primes in rational reconstruction. (English) Zbl 1326.13018 Math. Comput. 84, No. 296, 3013-3027 (2015). Reviewer: Thomas Kahle (Magdeburg) MSC: 13P10 68W30 52C05 68W10 PDF BibTeX XML Cite \textit{J. Böhm} et al., Math. Comput. 84, No. 296, 3013--3027 (2015; Zbl 1326.13018) Full Text: DOI arXiv
Furukado, Maki; Ito, Shunji; Saito, Asaki; Tamura, Jun-ichi; Yasutomi, Shin-ichi A new multidimensional slow continued fraction algorithm and stepped surface. (English) Zbl 1335.11055 Exp. Math. 23, No. 4, 390-410 (2014). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11J70 11Y65 37B10 52C22 68R15 PDF BibTeX XML Cite \textit{M. Furukado} et al., Exp. Math. 23, No. 4, 390--410 (2014; Zbl 1335.11055) Full Text: DOI arXiv
Kim, Dong Han; Lim, Seonhee; Nakada, Hitoshi; Natsui, Rie Farey maps, Diophantine approximation and Bruhat-Tits tree. (English) Zbl 1317.11076 Finite Fields Appl. 30, 14-32 (2014). Reviewer: Tonko Tonkov (Sofia) MSC: 11J61 11J70 37E25 PDF BibTeX XML Cite \textit{D. H. Kim} et al., Finite Fields Appl. 30, 14--32 (2014; Zbl 1317.11076) Full Text: DOI arXiv
Bonanno, Claudio; Isola, Stefano A thermodynamic approach to two-variable Ruelle and Selberg zeta functions via the Farey map. (English) Zbl 1312.37020 Nonlinearity 27, No. 5, 897-926 (2014). Reviewer: Jan Andres (Olomouc) MSC: 37C30 37D25 37E05 37D35 PDF BibTeX XML Cite \textit{C. Bonanno} and \textit{S. Isola}, Nonlinearity 27, No. 5, 897--926 (2014; Zbl 1312.37020) Full Text: DOI arXiv
Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie; Vallée, Brigitte Fine costs for Euclid’s algorithm on polynomials and Farey maps. (English) Zbl 1285.11102 Adv. Appl. Math. 54, 27-65 (2014). MSC: 11J70 11K50 68W40 11A05 62E20 11T55 PDF BibTeX XML Cite \textit{V. Berthé} et al., Adv. Appl. Math. 54, 27--65 (2014; Zbl 1285.11102) Full Text: DOI
Munday, Sara On the derivative of the \(\alpha\)-Farey-Minkowski function. (English) Zbl 1282.26005 Discrete Contin. Dyn. Syst. 34, No. 2, 709-732 (2014). Reviewer: Peter Massopust (München) MSC: 26A30 28A78 37C45 PDF BibTeX XML Cite \textit{S. Munday}, Discrete Contin. Dyn. Syst. 34, No. 2, 709--732 (2014; Zbl 1282.26005) Full Text: DOI arXiv
Luque, B.; Ballesteros, F. J.; Núñez, A. M.; Robledo, A. Quasiperiodic graphs: structural design, scaling and entropic properties. (English) Zbl 1268.37061 J. Nonlinear Sci. 23, No. 2, 335-342 (2013). MSC: 37E25 37E20 37B40 PDF BibTeX XML Cite \textit{B. Luque} et al., J. Nonlinear Sci. 23, No. 2, 335--342 (2013; Zbl 1268.37061) Full Text: DOI
Oku, Makito; Aihara, Kazuyuki Numerical analysis of transient and periodic dynamics in single and coupled Nagumo-Sato models. (English) Zbl 1270.37028 Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 6, Article ID 1230021, 15 p. (2012). MSC: 37E05 37M99 92B20 92C20 37D25 37D45 PDF BibTeX XML Cite \textit{M. Oku} and \textit{K. Aihara}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 6, Article ID 1230021, 15 p. (2012; Zbl 1270.37028) Full Text: DOI
Kesseböhmer, Marc; Munday, Sara; Stratmann, Bernd O. Strong renewal theorems and Lyapunov spectra for \(\alpha \)-Farey and \(\alpha \)-Lüroth systems. (English) Zbl 1263.37013 Ergodic Theory Dyn. Syst. 32, No. 3, 989-1017 (2012). Reviewer: Lingmin Liao (Créteil) MSC: 37A45 37E05 11K55 37D35 PDF BibTeX XML Cite \textit{M. Kesseböhmer} et al., Ergodic Theory Dyn. Syst. 32, No. 3, 989--1017 (2012; Zbl 1263.37013) Full Text: DOI arXiv
Kessböhmer, Marc; Stratmann, Bernd O. On the asymptotic behaviour of the Lebesgue measure of sum-level sets for continued fractions. (English) Zbl 1251.37013 Discrete Contin. Dyn. Syst. 32, No. 7, 2437-2451 (2012). Reviewer: Makoto Mori (Tokyo) MSC: 37A45 11J70 11J83 28A80 20H10 PDF BibTeX XML Cite \textit{M. Kessböhmer} and \textit{B. O. Stratmann}, Discrete Contin. Dyn. Syst. 32, No. 7, 2437--2451 (2012; Zbl 1251.37013) Full Text: DOI arXiv
Isola, Stefano From infinite ergodic theory to number theory (and possibly back). (English) Zbl 1230.37014 Chaos Solitons Fractals 44, No. 7, 467-479 (2011). Reviewer: Christoph Aistleitner (Graz) MSC: 37A45 37A40 11Z05 PDF BibTeX XML Cite \textit{S. Isola}, Chaos Solitons Fractals 44, No. 7, 467--479 (2011; Zbl 1230.37014) Full Text: DOI
Smillie, John; Ulcigrai, Corinna Beyond Sturmian sequences: coding linear trajectories in the regular octagon. (English) Zbl 1230.37021 Proc. Lond. Math. Soc. (3) 102, No. 2, 291-340 (2011). Reviewer: Wolfgang Steiner (Sydney) MSC: 37B10 11A55 37E35 PDF BibTeX XML Cite \textit{J. Smillie} and \textit{C. Ulcigrai}, Proc. Lond. Math. Soc. (3) 102, No. 2, 291--340 (2011; Zbl 1230.37021) Full Text: DOI arXiv
Avrutin, Viktor; Schanz, Michael; Gardini, Laura Calculation of bifurcation curves by map replacement. (English) Zbl 1204.37037 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 10, 3105-3135 (2010). MSC: 37E05 37G99 PDF BibTeX XML Cite \textit{V. Avrutin} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 10, 3105--3135 (2010; Zbl 1204.37037) Full Text: DOI
Kesseböhmer, Marc; Stratmann, Bernd O. Fractal analysis for sets of non-differentiability of Minkowski’s question mark function. (English) Zbl 1154.28001 J. Number Theory 128, No. 9, 2663-2686 (2008). Reviewer: Ryszard Pawlak (Łódź) MSC: 28A78 11K55 26A30 PDF BibTeX XML Cite \textit{M. Kesseböhmer} and \textit{B. O. Stratmann}, J. Number Theory 128, No. 9, 2663--2686 (2008; Zbl 1154.28001) Full Text: DOI arXiv
Panti, Giovanni Multidimensional continued fractions and a Minkowski function. (English) Zbl 1170.11020 Monatsh. Math. 154, No. 3, 247-264 (2008). Reviewer: Tomas Persson (Warszawa) MSC: 11J70 37A45 PDF BibTeX XML Cite \textit{G. Panti}, Monatsh. Math. 154, No. 3, 247--264 (2008; Zbl 1170.11020) Full Text: DOI arXiv
Matveev, Andrey O. Relative blocking in posets. (English) Zbl 1130.06001 J. Comb. Optim. 13, No. 4, 379-403 (2007). MSC: 06A07 05A05 11B57 90C27 PDF BibTeX XML Cite \textit{A. O. Matveev}, J. Comb. Optim. 13, No. 4, 379--403 (2007; Zbl 1130.06001) Full Text: DOI arXiv
Moshchevitin, Nikolai; Zhigljavsky, Anatoly Entropies of the partitions of the unit interval generated by the Farey tree. (English) Zbl 1065.11058 Acta Arith. 115, No. 1, 47-58 (2004). Reviewer: M. M. Dodson (Heslington) MSC: 11K60 11D68 11J70 37A45 37C30 PDF BibTeX XML Cite \textit{N. Moshchevitin} and \textit{A. Zhigljavsky}, Acta Arith. 115, No. 1, 47--58 (2004; Zbl 1065.11058) Full Text: DOI
Isola, Stefano On the spectrum of Farey and Gauss maps. (English) Zbl 1018.37019 Nonlinearity 15, No. 5, 1521-1539 (2002). Reviewer: Anne Broise-Alamichel (Orsay MSC: 37C30 11B57 37E05 47B38 PDF BibTeX XML Cite \textit{S. Isola}, Nonlinearity 15, No. 5, 1521--1539 (2002; Zbl 1018.37019) Full Text: DOI arXiv
Pronzato, Luc; Wynn, Henry P.; Zhigljavsky, Anatoly A. Analysis of performance of symmetric second-order line search algorithms through continued fractions. (English) Zbl 1022.37050 IMA J. Math. Control Inf. 18, No. 2, 281-296 (2001). MSC: 37N40 90C30 PDF BibTeX XML Cite \textit{L. Pronzato} et al., IMA J. Math. Control Inf. 18, No. 2, 281--296 (2001; Zbl 1022.37050) Full Text: DOI
Theunissen, M.; Nicolis, C.; Nicolis, G. Recurrence times in quasi-periodic motion: Statistical properties, role of cell size, parameter dependence. (English) Zbl 0949.37006 J. Stat. Phys. 94, No. 3-4, 437-467 (1999). Reviewer: Samir Musayev (Baku) MSC: 37C55 37E10 37A60 PDF BibTeX XML Cite \textit{M. Theunissen} et al., J. Stat. Phys. 94, No. 3--4, 437--467 (1999; Zbl 0949.37006) Full Text: DOI
Baney, Doug; Beslin, Scott; De Angelis, Valerio Farey tree and distribution of small denominators. (English) Zbl 0921.11039 Topol. Proc. 22, 23-35 (1997). Reviewer: Takao Komatsu (Tsu) MSC: 11K50 11B57 PDF BibTeX XML Cite \textit{D. Baney} et al., Topol. Proc. 22(Spring), 23--35 (1997; Zbl 0921.11039) Full Text: Link
Yamaguchi, Takahiro; Ohtagaki, Hirokazu The order of appearance of oscillation modes of a piecewise linear map. (English) Zbl 0955.37026 J. Phys. Soc. Japan 65, No. 11, 3500-3512 (1996). MSC: 37G99 PDF BibTeX XML Cite \textit{T. Yamaguchi} and \textit{H. Ohtagaki}, J. Phys. Soc. Japan 65, No. 11, 3500--3512 (1996; Zbl 0955.37026) Full Text: DOI
Brown, Gavin; Yin, Qinghe Metrical theory for Farey continued fractions. (English) Zbl 0880.11057 Osaka J. Math. 33, No. 4, 951-970 (1996). Reviewer: P.Szüsz (Glen) MSC: 11K50 PDF BibTeX XML Cite \textit{G. Brown} and \textit{Q. Yin}, Osaka J. Math. 33, No. 4, 951--970 (1996; Zbl 0880.11057)
Sasaki, Ryuji; Toki, Keisuke Determination of Fermat varieties with trivial Hasse-Witt map. An application of the Farey series. (English) Zbl 0707.14017 Acta Arith. 59, No. 4, 381-401 (1991). Reviewer: R.Sasaki; K.Toki MSC: 14G20 PDF BibTeX XML Cite \textit{R. Sasaki} and \textit{K. Toki}, Acta Arith. 59, No. 4, 381--401 (1991; Zbl 0707.14017) Full Text: DOI EuDML
Kim, Seunghwan; Ostlund, Stellan Universal scaling in circle maps. (English) Zbl 0701.57013 Physica D 39, No. 2-3, 365-392 (1989). Reviewer: I.Gumowski MSC: 57R35 57R45 PDF BibTeX XML Cite \textit{S. Kim} and \textit{S. Ostlund}, Physica D 39, No. 2--3, 365--392 (1989; Zbl 0701.57013) Full Text: DOI
Haucke, H.; Ecke, R. Mode-locking and chaos in Rayleigh-Bénard convection. (English) Zbl 0611.76062 Physica D 25, 307-329 (1987). MSC: 76E15 76Y05 81V99 76M99 76-04 70K50 PDF BibTeX XML Cite \textit{H. Haucke} and \textit{R. Ecke}, Physica D 25, 307--329 (1987; Zbl 0611.76062) Full Text: DOI