Échanges d'intervalles et surfaces de translation

Yoccoz, Jean-Christophe

Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 996, 23 p.

@incollection{AST_2009__326__387_0,
     author = {Yoccoz, Jean-Christophe},
     title = {\'Echanges d'intervalles et surfaces de translation},
     booktitle = {S\'eminaire Bourbaki Volume 2007/2008 Expos\'es 982-996},
     series = {Ast\'erisque},
     note = {talk:996},
     pages = {387--409},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {326},
     year = {2009},
     mrnumber = {2605330},
     zbl = {1203.37072},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2009__326__387_0/}
}

TY  - CHAP
AU  - Yoccoz, Jean-Christophe
TI  - Échanges d'intervalles et surfaces de translation
BT  - Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
AU  - Collectif
T3  - Astérisque
N1  - talk:996
PY  - 2009
SP  - 387
EP  - 409
IS  - 326
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2009__326__387_0/
LA  - fr
ID  - AST_2009__326__387_0
ER  -

%0 Book Section
%A Yoccoz, Jean-Christophe
%T Échanges d'intervalles et surfaces de translation
%B Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
%A Collectif
%S Astérisque
%Z talk:996
%D 2009
%P 387-409
%N 326
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2009__326__387_0/
%G fr
%F AST_2009__326__387_0

Yoccoz, Jean-Christophe. Échanges d'intervalles et surfaces de translation, dans Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 996, 23 p. http://archive.numdam.org/item/AST_2009__326__387_0/

Bibliographie
Cité par

[1] M. F. Atiyah - Riemann surfaces and spin structures, Ann. Sci. École Norm. Sup. 4 (1971), p. 47-62. | DOI | EuDML | Numdam | MR | Zbl

[2] A. Avila & G. Forni - Weak mixing for interval exchange transformations and translation flows, Ann. of Math. 165 (2007), p. 637-664. | DOI | MR | Zbl

[3] A. Avila, S. Gouëzel & J.-C. Yoccoz - Exponential mixing for the Teichmüller flow, Publ. Math. Inst. Hautes Études Sci. 104 (2006), p. 143-211. | DOI | EuDML | Numdam | MR | Zbl

[4] A. Avila & M. Viana - Simplicity of Lyapunov spectra : proof of the Zorich-Kontsevich conjecture, Acta Math. 198 (2007), p. 1-56. | DOI | MR | Zbl

[5] V. Baladi & B. Vallée - Exponential decay of correlations for surface semiflows without finite Markov partitions, Proc. Amer. Math. Soc. 133 (2005), p. 865-874. | DOI | MR | Zbl

[6] C. Bonatti, X. Gómez-Mont & M. Viana - Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), p. 579-624. | DOI | EuDML | Numdam | MR | Zbl

[7] C. Bonatti & M. Viana - Lyapunov exponents with multiplicity 1 for deterministic products of matrices, Ergodic Theory Dynam. Systems 24 (2004), p. 1295-1330. | DOI | MR | Zbl

[8] K. Calta - Veech surfaces and complete periodicity in genus two, J. Amer. Math. Soc. 17 (2004), p. 871-908. | DOI | MR | Zbl

[9] D. Dolgopyat - On decay of correlations in Anosov flows, Ann. of Math. 147 (1998), p. 357-390. | DOI | MR | Zbl

[10] A. Eskin & H. Masur - Asymptotic formulas on flat surfaces, Ergodic Theory Dynam. Systems 21 (2001), p. 443-478. | DOI | MR | Zbl

[11] A. Eskin, H. Masur & A. Zorich - Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants, Publ. Math. Inst. Hautes Études Sci. 97 (2003), p. 61-179. | DOI | EuDML | Numdam | MR | Zbl

[12] A. Eskin & A. Okounkov - Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001), p. 59-103. | DOI | MR | Zbl

[13] A. Eskin, A. Okounkov & R. Pandharipande - The theta characteristic of a branched covering, prepublication arXiv:math.AG/0312186. | DOI | MR | Zbl

[14] G. Forni - Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus, Ann. of Math. 146 (1997), p. 295-344. | DOI | MR | Zbl

[15] G. Forni -, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. of Math. 155 (2002), p. 1-103. | DOI | MR | Zbl

[16] H. Furstenberg - Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), p. 377-428. | DOI | MR | Zbl

[17] I. Y. Gol'Dsheĭd & G. A. Margulis - Lyapunov exponents of a product of random matrices, Uspekhi Mat. Nauk 44 (1989), p. 13-60. | MR | Zbl

[18] Y. Guivarc'H & A. Raugi - Products of random matrices : convergence theorems, in Random matrices and their applications (Brunswick, Maine, 1984), Contemp. Math., vol. 50, Amer. Math. Soc, 1986, p. 31-54. | DOI | MR | Zbl

[19] P. Hubert & E. Lanneau - Veech groups without parabolic elements, Duke Math. J. 133 (2006), p. 335-346. | DOI | MR | Zbl

[20] P. Hubert, E. Lanneau & M. Moller - The Arnoux-Yoccoz Teichmüller disc, prepublication arXiv:math/0611655. | DOI | MR | Zbl

[21] P. Hubert, E. Lanneau & M. Moller -, Completely periodic directions and orbit closures of many pseudo-Anosov Teichmüller discs in $q (1, 1, 1, 1)$ , prepublication arXiv:0707.0738. | MR | Zbl

[22] P. Hubert & S. Lelièvre - Noncongruence subgroups in $ℋ (2)$ , Int. Math. Res. Not. 2005 (2005), p. 47-64. | DOI | MR | Zbl

[23] P. Hubert & S. Lelièvre -, Prime arithmetic Teichmüller discs in $ℋ (2)$ , Israel J. Math. 151 (2006), p. 281-321. | DOI | MR | Zbl

[24] P. Hubert, H. Masur, T. A. Schmidt & A. Zorich - Problems on billiards, flat surfaces and translation surfaces, in Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc, 2006, p. 233-243. | DOI | MR | Zbl

[25] P. Hubert & T. A. Schmidt - Veech groups and polygonal coverings, J. Geom. Phys. 35 (2000), p. 75-91. | DOI | MR | Zbl

[26] P. Hubert & T. A. Schmidt -, Invariants of translation surfaces, Ann. Inst. Fourier (Grenoble) 51 (2001), p. 461-495. | DOI | EuDML | Numdam | MR | Zbl

[27] P. Hubert & T. A. Schmidt -, Infinitely generated Veech groups, Duke Math. J. 123 (2004), p. 49-69. | DOI | MR | Zbl

[28] P. Hubert & T. A. Schmidt -, Geometry of infinitely generated Veech groups, Conform. Geom. Dyn. 10 (2006), p. 1-20. | DOI | MR | Zbl

[29] P. Hubert & T. A. Schmidt -, An introduction to Veech surfaces, in Handbook of dynamical systems. Vol. 1B, Elsevier B. V., Amsterdam, 2006, p. 501-526. | MR | Zbl

[30] A. Katok - Interval exchange transformations and some special flows are not mixing, Israel J. Math. 35 (1980), p. 301-310. | DOI | MR | Zbl

[31] A. Katok & A. M. Stepin - Approximations in ergodic theory, Uspehi Mat. Nauk 22 (1967), p. 81-106. | MR | Zbl

[32] M. Keane - Interval exchange transformations, Math. Z. 141 (1975), p. 25-31. | DOI | EuDML | MR | Zbl

[33] M. Keane -, Non-ergodic interval exchange transformations, Israel J. Math. 26 (1977), p. 188-196. | DOI | MR | Zbl

[34] H. B. Keynes & D. Newton - A "minimal", non-uniquely ergodic interval exchange transformation, Math. Z. 148 (1976), p. 101-105. | DOI | EuDML | MR | Zbl

[35] M. Kontsevich - Lyapunov exponents and Hodge theory, in The mathematical beauty of physics (Saclay, 1996), Adv. Ser. Math. Phys., vol. 24, World Sci. Publ., River Edge, NJ, 1997, p. 318-332. | MR | Zbl

[36] M. Kontsevich & A. Zorich - Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003), p. 631-678. | DOI | MR | Zbl

[37] R. Krikorian - Déviations de moyennes ergodiques, flots de Teichmüller et cocycle de Kontsevich-Zorich (d'après Forni, Kontsevich, Zorich...), Séminaire Bourbaki, vol. 2003/04, exposé n° 927, Astérisque 299 (2005), p. 59-93. | EuDML | Numdam | MR | Zbl

[38] F. Ledrappier - Positivity of the exponent for stationary sequences of matrices, in Lyapunov exponents (Bremen, 1984), Lecture Notes in Math., vol. 1186, Springer, 1986, p. 56-73. | DOI | MR | Zbl

[39] S. Marmi, P. Moussa & J.-C. Yoccoz - The cohomological equation for Roth-type interval exchange maps, J. Amer. Math. Soc. 18 (2005), p. 823-872. | DOI | MR | Zbl

[40] H. Masur - Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982), p. 169-200. | DOI | MR | Zbl

[41] C. T. Mcmullen - Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc. 16 (2003), p. 857-885. | DOI | MR | Zbl

[42] C. T. Mcmullen -, Teichmüller geodesics of infinite complexity, Acta Math. 191 (2003), p. 191-223. | DOI | MR | Zbl

[43] C. T. Mcmullen -, Teichmüller curves in genus two : discriminant and spin, Math. Ann. 333 (2005), p. 87-130. | DOI | MR | Zbl

[44] C. T. Mcmullen -, Teichmüller curves in genus two : the decagon and beyond, J. reine angew. Math. 582 (2005), p. 173-199. | DOI | MR | Zbl

[45] C. T. Mcmullen -, Prym varieties and Teichmüller curves, Duke Math. J. 133 (2006), p. 569-590. | DOI | MR | Zbl

[46] C. T. Mcmullen -, Teichmüller curves in genus two : torsion divisors and ratios of sines, Invent. Math. 165 (2006), p. 651-672. | DOI | MR | Zbl

[47] C. T. Mcmullen -, Dynamics of ${SL}_{2} (ℝ)$ over moduli space in genus two, Ann. of Math. 165 (2007), p. 397-456. | DOI | MR | Zbl

[48] J. Milnor - Remarks concerning spin manifolds, in Differential and Combinatorial Topology (in Honor of Marston Morse), Princeton, 1965. | MR | Zbl

[49] A. Nogueira & D. Rudolph - Topological weak-mixing of interval exchange maps, Ergodic Theory Dynam. Systems 17 (1997), p. 1183-1209. | DOI | MR | Zbl

[50] V. I. Oseledets - A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), p. 197-231. | MR | Zbl

[51] G. Rauzy - Échanges d'intervalles et transformations induites, Acta Arith. 34 (1979), p. 315-328. | DOI | EuDML | MR | Zbl

[52] W. A. Veech - Interval exchange transformations, J. Analyse Math. 33 (1978), p. 222-272. | DOI | MR | Zbl

[53] W. A. Veech -, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. 115 (1982), p. 201-242. | DOI | MR | Zbl

[54] W. A. Veech -, The metric theory of interval exchange transformations. I. Generic spectral properties, Amer. J. Math. 106 (1984), p. 1331-1359. | DOI | MR | Zbl

[55] W. A. Veech -, The metric theory of interval exchange transformations. II. Approximation by primitive interval exchanges, Amer. J. Math. 106 (1984), p. 1361-1387. | DOI | MR | Zbl

[56] W. A. Veech -, The Teichmüller geodesic flow, Ann. of Math. 124 (1986), p. 441-530. | DOI | MR | Zbl

[57] J.-C. Yoccoz - Continued fraction algorithms for interval exchange maps : an introduction, in Frontiers in number theory, physics, and geometry. I, Springer, 2006, p. 401-435. | DOI | MR | Zbl

[58] J.-C. Yoccoz -, Échanges d'intervalles, cours au Collège de France, http://www.college-de-france.fr/site/jean-christophe-yoccoz/course-2008-2009.htm

[59] A. Zorich - Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents, Ann. Inst. Fourier (Grenoble) 46 (1996), p. 325-370. | DOI | EuDML | Numdam | MR | Zbl

[60] A. Zorich -, Deviation for interval exchange transformations, Ergodic Theory Dynam. Systems 17 (1997), p. 1477-1499. | DOI | MR | Zbl

[61] A. Zorich -, How do the leaves of a closed 1-form wind around a surface ?, in Pseudoperiodic topology, Amer. Math. Soc. Transl. Ser. 2, vol. 197, Amer. Math. Soc, 1999, p. 135-178. | MR | Zbl

[62] A. Zorich -, Flat surfaces, in Frontiers in number theory, physics, and geometry. I, Springer, 2006, p. 437-583. | DOI | MR | Zbl