Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
Arnoux, Pierre ; Nogueira, Arnaldo
Annales scientifiques de l'École Normale Supérieure, Tome 26 (1993), p. 645-664 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1993_4_26_6_645_0,
     author = {Arnoux, Pierre and Nogueira, Arnaldo},
     title = {Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {26},
     year = {1993},
     pages = {645-664},
     doi = {10.24033/asens.1682},
     mrnumber = {95h:11076},
     zbl = {0801.11036},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1993_4_26_6_645_0}
}

Arnoux, Pierre; Nogueira, Arnaldo. Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles. Annales scientifiques de l'École Normale Supérieure, Tome 26 (1993) pp. 645-664. doi : 10.24033/asens.1682. http://gdmltest.u-ga.fr/item/ASENS_1993_4_26_6_645_0/

[AF1] R. Adler et L. Flatto, The Backward Continued Fraction Map and Geodesic Flow (Ergod. Th. & Dynam. Sys., vol. 4, 1984, p. 487-492). | MR 86h:58116 | Zbl 0563.58019

[AF2] R. Adler et L. Flatto, Geodesic Flows, Interval Maps and Symbolic Dynamics (Bull. Amer. Math. Soc., vol. 25, 1991, p. 229-334). | MR 92b:58172 | Zbl 0802.58037

[Ar] G. Arsac, L'origine de la démonstration : essai d'épistémologie didactique, Recherches en didactique des mathématiques, vol. 8, 1987, p. 267-312.

[BKS] Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, edited by T. BEDFORD, M. KEANE and C, Series, Oxford Science Publications, Oxford, 1991. | Zbl 0743.00040

[Bi] P. Billingsley, Ergodic Theory and Information, John Wiley & Sons, New York, 1965. | MR 33 #254 | Zbl 0141.16702

[Br] A. J. Brentjes, Multi-Dimensional Continued Fractions Algorithms, Mathematical Centre Tracts 145, Amsterdam, 1981. | MR 83b:10038 | Zbl 0471.10024

[Fa] C. Faivre, Distribution des constantes de Lévy des nombres quadratiques, Thèse, Université de Provence, 1991.

[INT] S. Ito, H. Nakada et S. Tanaka, On the Invariant Measure for the Transformations Associated with some Real Continued Fractions, Keio Engeneering Reports, vol. 30, 1977, p. 159-175. | MR 58 #16574 | Zbl 0412.10037

[Ja] H. Jager, The Distribution of Certain Sequences connected with the Continued Fraction (Indag. Math., vol. 48, 1986, p. 61-69). | MR 87g:11092 | Zbl 0588.10061

[Kh] A. Ya. Khinchin, Continued Fractions, The University of Chicago Press, Chicago, 1964. | MR 161833 | Zbl 0117.28601

[Le] P. Levy, Sur le développement en fraction continue d'un nombre choisi au hasard, Compositio Mathematica, vol. 3, 1936, p. 286-303. | JFM 62.0246.01 | Numdam | MR 1556945 | Zbl 0014.26803

[Mo] B. Morin, Structure géométrique d'un ensemble de surfaces : l'ensemble des métriques à courbure nulle du tore, dans Encyclopédie philosophique, Presses Universitaires de France, Paris.

[Na] H. Nakada, Metrical Theory for a Class of Continued Fraction Transformations and Their Natural Extensions (Tokyo J. Math., vol. 4, 1981, p. 399-426). | MR 646050 | MR 83k:10095 | Zbl 0479.10029

[Po] M. Pollicott, Distribution of Closed Geodesics on the Modular Surface and Quadratic Irrationals (Bull. Soc. Math. Fr., vol. 114, 1986, p. 431-446). | Numdam | MR 882589 | MR 88j:58102 | Zbl 0624.58019

[Sc1] F. Schweiger, The Metrical Theory of Jacobi-Perron Algorithm (Lecture Notes Math., vol. 334, Springer Verlag, Berlin, 1973). | MR 345925 | MR 49 #10654 | Zbl 0287.10041

[Sc2] F. Schweiger, Ergodische Eigenschaften der Algorithmen von Brun und Selmer (S. Ber. Österr. Akad. Wiss. Math.-naturw. K1, Abt. II, vol. 191, 1982, p. 325-329). | MR 716668 | MR 84m:10046 | Zbl 0518.10060

[Sc3] F. Schweiger, Invariant Measures for Maps of Continued Fraction Type [J. Number Theory, 1990, (à paraître)]. | MR 1129566 | Zbl 0748.11037

[Sc4] F. Schweiger, Ergodic Properties of Fibered Systems, Prépublication de l'université de Salzburg, 1989.

[Se] C. Series, Geometrical Markov Coding of Geodesics on Surfaces of Constant Negative Curvature, (Ergod. Th. & Dynam. Sys., vol. 6, 1986, p. 601-625). | MR 873435 | MR 88k:58130 | Zbl 0593.58033

[Ve1] W. A. Veech, Gauss Measures for Transformations on the space of interval Exchange Maps (Ann. of Math., vol. 115, 1982, p. 201-242). | MR 644019 | MR 83g:28036b | Zbl 0486.28014

[Ve2] W. A. Veech, The Teichmüller Geodesic flow (Ann. of Math., vol. 124, 1986, p. 441-530). | MR 866707 | MR 88g:58153 | Zbl 0658.32016