Fractions continues multidimensionnelles et lois stables

Anne Broise

Bulletin de la Société Mathématique de France (1996)

  • Volume: 124, Issue: 1, page 97-139
  • ISSN: 0037-9484

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Broise, Anne. "Fractions continues multidimensionnelles et lois stables." Bulletin de la Société Mathématique de France 124.1 (1996): 97-139. <http://eudml.org/doc/87736>.

@article{Broise1996,
author = {Broise, Anne},
journal = {Bulletin de la Société Mathématique de France},
keywords = {invariant probability measure; multidimensional continued fraction expansion; Jacobi-Perron algorithm; simultaneous rational approximations; stable distribution},
language = {fre},
number = {1},
pages = {97-139},
publisher = {Société mathématique de France},
title = {Fractions continues multidimensionnelles et lois stables},
url = {http://eudml.org/doc/87736},
volume = {124},
year = {1996},
}

TY - JOUR
AU - Broise, Anne
TI - Fractions continues multidimensionnelles et lois stables
JO - Bulletin de la Société Mathématique de France
PY - 1996
PB - Société mathématique de France
VL - 124
IS - 1
SP - 97
EP - 139
LA - fre
KW - invariant probability measure; multidimensional continued fraction expansion; Jacobi-Perron algorithm; simultaneous rational approximations; stable distribution
UR - http://eudml.org/doc/87736
ER -

References

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  5. [Bre] BRENTJES (A.J.). — Multi-dimensional continued fraction algorithms. — Mathematical centre tracts 145, Mathematisch Centrum, Amsterdam, 1981. Zbl0471.10024MR83b:10038
  6. [B-K] BUSEMANN (H.) and KELLY (P.). — Projective geometry and projective metrics. — Academic Press, New York, 1953. Zbl0052.37305MR14,1008e
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  10. [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. Zbl0784.60076MR94a:58157
  11. [Kh] KHINTCHINE (A. Ya.). — Continued Fractions. — The University of Chicago Press, Chicago, 1964. Zbl0117.28601
  12. [K] KRASNOLSELSKII (M.). — Positive solutions of operator equations. — Groningen Noodshoff, 1964. 
  13. [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. 
  14. [L1] LÉVY (P.). — Théorie de l'addition des variables aléatoires. — Gauthier-Villars, Paris, 1937. Zbl0016.17003JFM63.0490.04
  15. [L2] LÉVY (P.). — Sur le développement en fraction continue d'un nombre choisi au hasard, Compositio Math., t. 3, 1936, p. 286-303. Zbl0014.26803JFM62.0246.01
  16. [Ma] MAYER (D.). — Approach to equilibrium for locally expanding maps in Rk, Comm. Math. Phys., t. 95, 1984, p. 1-15. Zbl0577.58022MR86d:58069
  17. [Mo] MONTEL (P.). — Leçons sur les familles normales de fonctions analytiques et leur application, chap. I et IX. — Gauthier-Villar Paris, 1927. JFM53.0303.02
  18. [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. Zbl0518.60033MR84m:60032
  19. [S] SCHWEIGER (F.). — The metrical theory of Jacobi-Perron algorithm, Lecture Notes in Mathematics 334, Springer 1973. Zbl0287.10041MR49 #10654
  20. [Z] ZYGMUND (A.). — Trigonometrical series, vol. I. — Second edition, Cambridge University Press, 1959. Zbl0095.27501

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