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Table of contents for this issue | Next article Ferenczi, Sébastien; Holton, Charles; Zamboni, Luca Q. Structure of three interval exchange transformations I : an arithmetic study. Annales de l'institut Fourier, 51 no. 4 (2001), p. 861-901 Full text djvu | pdf | Reviews MR 1849209 | Zbl 1029.11036 | 2 citations in Numdam Class. Math.: 11J70, 11J13, 37A05 stable URL: http://www.numdam.org/item?id=AIF_2001__51_4_861_0 Lookup this article on the publisher's site Abstract Bibliography [2] V.I. Arnold, A-graded algebras and continued fractions, Comm. Pure Applied Math. [3] P. Arnoux, Un exemple de semi-conjugaison entre un échange d'intervalles et une translation sur le tore (in French), Bull. Soc. Math. France Numdam | MR 1005392 | Zbl 0703.58045 [4] P. Arnoux, V. Berthe & S. Ito, Discrete planes, ${\Bbb Z}^2$-actions, Jacobi-Perron algorithm and substitutions, Preprint, [5] P. Arnoux & G. Rauzy, Représentation géométrique de suites de complexité $2n+1$, Bull. Soc. Math. France Numdam | MR 1116845 | Zbl 0789.28011 [6] L. Bernstein, The Jacobi-Perron algorithm; its theory and applications, [7] V. Berthe & L. Vuillon, Tilings and rotations: a two-dimensional generalization of Sturmian sequences, Discrete Math. [8] M. Boshernitzan & C. Carroll, An extension of Lagrange's theorem to interval exchange transformations over quadratic fields, J. Anal. Math. [9] A.J. Brentjes, Multi-dimensional continued fraction algorithms, Math. Centre Tracts, Amsterdam [10] E. Burger, On simultaneous diophantine approximation in the vector space $\rats + \rats \alpha$, J. Number Theory [11] E. Burger, On real quadratic number fields and simultaneous diophantine approximation, Monats. Math. [12] J. Cassaigne, S. Ferenczi & L.Q. Zamboni, Imbalances in Arnoux-Rauzy sequences, Ann. Inst. Fourier Numdam | MR 1799745 | Zbl 1004.37008 [13] N. Chekhova, P. Hubert & A. Messaoudi, Propriétés combinatoires, ergodiques et arithmétiques de la substitution de tribonacci, J. Théorie des Nombres de Bordeaux ( Numdam | MR 1879664 | Zbl 1038.37010 [14] E.M. Coven & G.A. Hedlund, Sequences with minimal block growth, Math. Systems Theory [15] A. del Junco, A family of counterexamples in ergodic theory, Israël J. Math. [16] S. Ferenczi, C. Holton & L.Q. Zamboni, Structure of three-interval exchange transformations II: a combinatorial description of the trajectories, Preprint, 32pp., [17] S. Ferenczi, C. Holton & L.Q. Zamboni, Structure of three-interval exchange transformations III: ergodic and spectral properties, Preprint, 29 pp., [18] T. Garrity, On periodic sequences for algebraic numbers, , http://front.math.ucdavis.edu/math.NT/9906016, arXiv | Zbl 1015.11031 [19] Y. Hara-Mimachi & S. Ito, A characterization of real quadratic numbers by diophantine algorithms, Tokyo J. Math. [20] G.H. Hardy & E.M. Wright, An introduction to the theory of numbers, [21] C. Hermite, Letter to C.D.J. Jacobi, J. reine. angew Math. [22] A. Hurwitz, Über eine besondere Art der Kettenbruchentwicklung reeller Grössen, Acta Math. [23] A.B. Katok & A.M. Stepin, Approximations in ergodic theory, Usp. Math. Nauk. [25] E. Korkina, La périodicité des fractions continues multidimensionnelles, C.R. Acad. Sci. Paris, Série I [26] C. Kraaikamp, A new class of continued fraction expansions, Acta Arith. [27] J.L. Lagrange, Sur la solution des problèmes indéterminés du second degré, Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Berlin Article [28] H. Minkowski, Ein Kriterium für algebraishcen Zahlen, Nachrichten der K. Gesellschaft der Wissenschaften zu Göttingen Mathematisch-physikalische Klasse p. [29] H. Minkowski, Über periodische Approximationen algebraischer Zahlen, Acta Math. [30] M. Morse & G.A. Hedlund, Symbolic dynamics, Amer. J. Math. [31] M. Morse & G.A. Hedlund, Symbolic dynamics II: Sturmian sequences, Amer. J. Math. [32] O. Perron, Die Lehre von den Kettenbrüchen (in German), 2nd ed., [33] G. Rauzy, Une généralization du développement en fraction continue, Numdam [34] G. Rauzy, Échanges d'intervalles et transformations induites, Acta Arith. Article | MR 543205 | Zbl 0414.28018 [35] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France Numdam | MR 667748 | Zbl 0522.10032 [36] R. RISLEY & L.Q. ZAMBONI, A generalization of Sturmian sequences; combinatorial properties and transcendence, Acta Arith. [37] F. Schweiger, The metrical theory of Jacobi-Perron algorithm, [38] F. Schweiger, Ergodic Theory of Fibred Systems and Metric Number Theory, [39] C. Szekeres, Multidimensional continued fractions, Ann. Univ. Sci. Budapest Sect. Math. [40] W. Veech, Interval exchange transformations, J. Anal. Math. [41] W. Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. [42] W. Veech, The metric theory of interval exchange transformations I, II, III, Amer. J. Math. [43] N. Wozny & L.Q. Zamboni, Frequencies of factors in Arnoux-Rauzy sequences, Acta Arith. [44] L.Q. Zamboni, Une généralisation du théorème de Lagrange sur le développement en fraction continue, C.R. Acad. Sci. Paris, Série I [24] F. Klein, Sur une représentation géométrique du développement en fraction continue ordinaire, Nouv. Ann. Math. [<L>23</L>] A.B. Katok & A.M. Stepin, Approximations in ergodic theory, Russian Math. Surveys |
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