Fractions continues multidimensionnelles et lois stables
Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 1, pp. 97-139. 
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Broise, Anne. Fractions continues multidimensionnelles et lois stables. Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 1, pp. 97-139. doi : 10.24033/bsmf.2277. https://www.numdam.org/articles/10.24033/bsmf.2277/

[Be] Bernstein (L.). - The Jacobi-Perron algorithm, its theory and application, Lecture Notes in Mathematics 207, Springer 1971. | MR | Zbl

[B-G-T] Bingham (N.H.), Goldie (C.M.) et Teugels (J.-L.). - Regular variation. - Encyclopedia of Mathematics and its Applications, 1987. | MR | Zbl

[Br] Breiman (L.). - Probability. - Addison-Wesley, 1968. | MR | Zbl

[Bi] Birkhoff (G.). - Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc., t. 104, 1965, p. 507-512. | MR

[Bre] Brentjes (A.J.). - Multi-dimensional continued fraction algorithms. - Mathematical centre tracts 145, Mathematisch Centrum, Amsterdam, 1981. | MR | Zbl

[B-K] Busemann (H.) and Kelly (P.). - Projective geometry and projective metrics. - Academic Press, New York, 1953. | MR | Zbl

[D-S] Dunford (N.) et Schwartz (J.T.). - Linear operators, part I. - Interscience New York, 1958. | Zbl

[F] Feller (W.). - An Introduction to probability theory and its applications Vol. II. - Willey, New York, 1966. | MR | Zbl

[G-H] Guivarc'H (Y.) et Hardy (J.). - Théorèmes limites pour une classe de chaîne de Markov et applications aux difféomorphismes d'Anosov, Ann. Inst. H. Poincaré, t. 24, 1988, p. 73-98. | EuDML | Numdam | MR | Zbl

[G-L] Guivarc'H (Y.) and Le Jan (Y.). - Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions, Ann. Sci. École Norm. Sup., t. 26, 1993, p. 23-50. | Numdam | MR | Zbl

[Kh] Khintchine (A. Ya.). - Continued Fractions. - The University of Chicago Press, Chicago, 1964. | Zbl

[K] Krasnolselskii (M.). - Positive solutions of operator equations. - Groningen Noodshoff, 1964.

[K-R] Krein (M.G.) and Rutman (M.A.). - Linear operators leaving invariant a cone in a Banach space, Translations A.M.S., series one, vol. 10, Functional Analysis and Measure Theory, p. 199-325, 1962.

[L1] Lévy (P.). - Théorie de l'addition des variables aléatoires. - Gauthier-Villars, Paris, 1937. | JFM | Zbl

[L2] Lévy (P.). - Sur le développement en fraction continue d'un nombre choisi au hasard, Compositio Math., t. 3, 1936, p. 286-303. | JFM | Numdam | Zbl

[Ma] Mayer (D.). - Approach to equilibrium for locally expanding maps in Rk, Comm. Math. Phys., t. 95, 1984, p. 1-15. | MR | Zbl

[Mo] Montel (P.). - Leçons sur les familles normales de fonctions analytiques et leur application, chap. I et IX. - Gauthier-Villar Paris, 1927. | JFM

[R] Rousseau-Egèle (J.). - Un théorème de la limite locale pour une classe de transformations dilatantes et monotones par morceaux, Ann. Probab., t. 3, 1983, p. 772-788. | MR | Zbl

[S] Schweiger (F.). - The metrical theory of Jacobi-Perron algorithm, Lecture Notes in Mathematics 334, Springer 1973. | MR | Zbl

[Z] Zygmund (A.). - Trigonometrical series, vol. I. - Second edition, Cambridge University Press, 1959.

  • Berthé, V.; Dajani, K.; Kalle, C.; Krawczyk, E.; Kuru, H.; Thevis, A. Rational approximations, multidimensional continued fractions, and lattice reduction, 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, 2024, pp. 111-154 | DOI:10.1007/978-3-031-52163-8_5 | Zbl:7919514
  • Berthé, Valérie; Steiner, Wolfgang; Thuswaldner, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations, Journal of the European Mathematical Society (JEMS), Volume 25 (2023) no. 12, pp. 4997-5057 | DOI:10.4171/jems/1300 | Zbl:1533.37040
  • Berthé, Valérie; Lee, Jungwon Dynamics of Ostrowski skew-product. I: Limit laws and Hausdorff dimensions, Transactions of the American Mathematical Society, Volume 376 (2023) no. 11, pp. 7947-7982 | DOI:10.1090/tran/9022 | Zbl:1546.11114
  • Berthé, V. Numeration and discrete dynamical systems, Computing, Volume 94 (2012) no. 2-4, pp. 369-387 | DOI:10.1007/s00607-011-0181-9 | Zbl:1269.11009
  • Zweimüller, Roland Kuzmin, coupling, cones, and exponential mixing, Forum Mathematicum, Volume 16 (2004) no. 3 | DOI:10.1515/form.2004.021
  • Arnoux, Pierre; Berthé, Valérie; Ito, Shunji Discrete planes, Z2-actions, Jacobi-Perron algorithm and substitutions, Annales de l'Institut Fourier, Volume 52 (2002) no. 2, pp. 305-349 | DOI:10.5802/aif.1889 | Zbl:1017.11006
  • 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), Annales de l'Institut Fourier, Volume 51 (2001) no. 3, pp. 565-686 | DOI:10.5802/aif.1832 | Zbl:1012.11060
  • Murray, Rua Existence, mixing and approximation of invariant densities for expanding maps on Rr, Nonlinear Analysis. Theory, Methods Applications. Series A: Theory and Methods, Volume 45 (2001) no. 1, pp. 37-72 | DOI:10.1016/s0362-546x(99)00329-6 | Zbl:1193.37029
  • Fisher, Albert M; Lopes, Artur Exact bounds for the polynomial decay of correlation, 1/fnoise and the CLT for the equilibrium state of a non-Hölder potential, Nonlinearity, Volume 14 (2001) no. 5, p. 1071 | DOI:10.1088/0951-7715/14/5/310
  • Arnoux, Pierre; Hubert, Pascal Continued fractions on the Veech surfaces, Journal d'Analyse Mathématique, Volume 81 (2000), pp. 35-64 | DOI:10.1007/bf02788985 | Zbl:1029.11035
  • Yuri, Michiko Statistical properties for nonhyperbolic maps with finite range structure, Transactions of the American Mathematical Society, Volume 352 (2000) no. 5, pp. 2369-2388 | DOI:10.1090/s0002-9947-00-02579-4 | Zbl:0981.11028
  • Baladi, V; Nogueira, A Lyapunov exponents for non-classical multidimensional continued fraction algorithms, Nonlinearity, Volume 9 (1996) no. 6, p. 1529 | DOI:10.1088/0951-7715/9/6/008

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