Une invitation aux surfaces de dilatation
Selim Ghazouani1
1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, (U.K.)
Séminaire de théorie spectrale et géométrie, Volume 35 (2017-2019), pp. 69-107.

Ce texte est une introduction aux emphsurfaces de dilatation. On tente d’exposer les aspects géométriques et dynamiques du sujet : les espaces de modules, les feuilletages directionnels et la dynamique du flot de Teichmüller.

Published online:
DOI: 10.5802/tsg.364
Selim Ghazouani 1

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, (U.K.) 
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Selim Ghazouani. Une invitation aux surfaces de dilatation. Séminaire de théorie spectrale et géométrie, Volume 35 (2017-2019), pp. 69-107. doi : 10.5802/tsg.364. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.364/

[1] Lars V. Ahlfors Fundamental polyhedrons and limit point sets of Kleinian groups, Proc. Natl. Acad. Sci. USA, Volume 55 (1966), pp. 251-254 | DOI | MR | Zbl

[2] Vladimir I. Arnol’d Small denominators. I. Mapping the circle onto itself, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 25 (1961), pp. 21-86 | MR

[3] Adrien Boulanger; Charles Fougeron; Selim Ghazouani Cascades in the dynamics of affine interval exchange transformations (2017) (https://arxiv.org/abs/1701.02332 , to appear at Ergodic Theory and Dynamical Systems) | Zbl

[4] Adrien Boulanger; Selim Ghazouani Sl 2 (ℝ)-dynamics on the moduli space of one-holed tori (2019) (https://arxiv.org/abs/1912.08154)

[5] Joshua Bowman; Slade Sanderson Angels’ staircases, Sturmian sequences, and trajectories on homothety surfaces (https://arxiv.org/abs/1806.04129) | Zbl

[6] Xavier Bressaud; Pascal Hubert; Alejandro Maass Persistence of wandering intervals in self-similar affine interval exchange transformations, Ergodic Theory Dyn. Syst., Volume 30 (2010) no. 3, pp. 665-686 | DOI | MR | Zbl

[7] Ricardo Camelier; Carlos Gutierrez Affine interval exchange transformations with wandering intervals, Ergodic Theory Dyn. Syst., Volume 17 (1997) no. 6, pp. 1315-1338 | DOI | MR | Zbl

[8] David K. Campbell; Roza Galeeva; Charles Tresser; David J. Uherka Piecewise linear models for the quasiperiodic transition to chaos, Chaos, Volume 6 (1996) no. 2, pp. 121-154 | DOI | MR | Zbl

[9] Thomas M. Cherry Analytic Quasi-Periodic Curves of Discontinuous Type on a Torus, Proc. Lond. Math. Soc., Volume 44 (1938) no. 3, pp. 175-215 | DOI | MR | Zbl

[10] Milton Cobo Piece-wise affine maps conjugate to interval exchanges, Ergodic Theory Dyn. Syst., Volume 22 (2002) no. 2, pp. 375-407 | DOI | MR | Zbl

[11] Kleyber Cunha; Daniel Smania Renormalization for piecewise smooth homeomorphisms on the circle, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 30 (2013) no. 3, pp. 441-462 | DOI | Numdam | MR | Zbl

[12] David Dumas Complex projective structures, Handbook of Teichmüller theory. Vol. II (IRMA Lectures in Mathematics and Theoretical Physics), Volume 13, European Mathematical Society, 2009, pp. 455-508 | DOI | MR | Zbl

[13] Eduard Duryev; Carlos Fougeron; Selim Ghazouani Affine surfaces and their Veech groups (2016) (https://arxiv.org/abs/1609.02130 To appear at Journal of Modern Dynamics) | Zbl

[14] Giovanni Forni Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. Math., Volume 155 (2002) no. 1, pp. 1-103 | DOI | MR | Zbl

[15] Selim Ghazouani Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms (2018) (https ://arxiv.org/abs/1803.10129) | Zbl

[16] Michael-Robert Herman Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math., Inst. Hautes Étud. Sci. (1979) no. 49, pp. 5-233 | DOI | Numdam | MR | Zbl

[17] D. V. Khmelev Rational rotation numbers for homeomorphisms with several break-type singularities, Ergodic Theory Dyn. Syst., Volume 25 (2005) no. 2, pp. 553-592 | DOI | MR | Zbl

[18] Isabelle Liousse Dynamique générique des feuilletages transversalement affines des surfaces, Bull. Soc. Math. Fr., Volume 123 (1995) no. 4, pp. 493-516 | DOI | Numdam | MR | Zbl

[19] Stephano Marmi; Pierre Moussa; Jean-Christophe Yoccoz Affine interval exchange maps with a wandering interval, Proc. Lond. Math. Soc., Volume 100 (2010) no. 3, pp. 639-669 | DOI | MR | Zbl

[20] Curtis T. McMullen; Amir Mohammadi; Hee Oh Geodesic planes in hyperbolic 3-manifolds, Invent. Math., Volume 209 (2017) no. 2, pp. 425-461 | DOI | MR | Zbl

[21] William A. Veech Flat surfaces, Am. J. Math., Volume 115 (1993) no. 3, pp. 589-689 | DOI | MR | Zbl

[22] Jean-Christophe Yoccoz Échanges d’intervalles et surfaces de translation, Séminaire Bourbaki. Vol. 2007/2008 (Astérisque), Société Mathématique de France, 2009 no. 326, pp. 387-410 | MR | Zbl

[23] Anton Zorich Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents, Ann. Inst. Fourier, Volume 46 (1996) no. 2, pp. 325-370 | DOI | Numdam | MR | Zbl

[24] Anton Zorich Flat surfaces, Frontiers in number theory, physics, and geometry. I. On random matrices, zeta functions, and dynamical systems, Springer, 2006, pp. 437-583 | DOI | MR | Zbl

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