### A Fundamental Domain for ${V}_{3}$  [ Un domaine fondamental pour ${V}_{3}$ ] (2010)

Mémoires de la Société Mathématique de France, Tome 121 (2010) ii-139 p
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doi : 10.24033/msmf.433
URL stable : http://www.numdam.org/item?id=MSMF_2010_2_121__1_0

### Bibliographie

[1] M. Aspenberg & M. Yampolsky« Mating non-renormalizable quadratic polynomials », Comm. Math. Phys. 287 (2009), p. 1–40. Zbl 1187.37065 | MR 2480740

[2] A. Avila, J. Kahn, M. Lyubich & W. Shen« Combinatorial rigidity for unicritical polynomials », Ann. of Math. 170 (2009), p. 783–797. Zbl 1204.37047 | MR 2552107

[3] B. H. Bowditch« Length bounds on curves arising from tight geodesics », Geom. Funct. Anal. 17 (2007), p. 1001–1042. Zbl 1148.57024 | MR 2373010

[4] —, « End invariants of hyperbolic 3-manifolds », preprint http://www.warwick.ac.uk/~masgak/preprints.html.

[5] —, « Geometric models for hyperbolic 3-manifolds », preprint http://www.warwick.ac.uk/~masgak/preprints.html.

[6] B. Branner & J. H. Hubbard« The iteration of cubic polynomials. I. The global topology of parameter space », Acta Math. 160 (1988), p. 143–206. Zbl 0668.30008 | MR 945011

[7] —, « The iteration of cubic polynomials. II. Patterns and parapatterns », Acta Math. 169 (1992), p. 229–325. Zbl 0812.30008 | MR 1194004

[8] J. Brock, R. Canary & Y. Minsky« The classification of Kleinian surface groups II: The ending laminations conjecture », preprint http://www.math.yale.edu/users/yair/research, 2004. MR 2925381

[9] J. Brock, B. K., R. Evans & J. Souto – in preparation.

[10] A. Douady & J. H. Hubbard« Études dynamiques des polynômes complexes, avec la collaboration de P. Lavaurs, Tan Lei, P. Sentenac. Parties I and II », Publications Mathématiques d’Orsay, 1985. MR 812271

[11] —, « A proof of Thurston’s topological characterization of rational functions », Acta Math. 171 (1993), p. 263–297. Zbl 0806.30027 | MR 1251582

[12] J. H. Hubbard« Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz », in Topological methods in modern mathematics (Stony Brook, NY, 1991), Publish or Perish, 1993, p. 467–511. Zbl 0797.58049 | MR 1215974

[13] J. Kahn« A priori bounds for some infinitely renormalizable quadratics: I. Bounded primitive combinatorics », preprint http://front.math.ucdavis.edu/math.DS/0609045.

[14] J. Kahn & M. Lyubich« A priori bounds for some infinitely renormalizable quadratics. II. Decorations », Ann. Sci. Éc. Norm. Supér. 41 (2008), p. 57–84. Numdam | Zbl 1156.37311 | | MR 2423310

[15] —, « Local connectivity of julia sets for unicritical polynomials », Ann. of Math. 170 (2009), p. 413–426. Zbl 1180.37072

[16] —, « A priori bounds for some infinitely renormalizable quadratics. III. Molecules », in Complex dynamics (D. Schleicher & N. Selinger, éds.), A K Peters, 2009, p. 229–254. Zbl 1180.37069

[17] —, « The quasi-additivity law in conformal geometry », Ann. of Math. 169 (2009), p. 561–593. Zbl 1203.30011

[18] J. Kiwi« Rational laminations of complex polynomials », in Laminations and foliations in dynamics, geometry and topology (Stony Brook, NY, 1998) (M. Lyubich et al., éds.), Contemp. Math., vol. 269, Amer. Math. Soc., 2001, Volume arising from conference, SUNY at Stony Brook, 1998, p. 111–154. Zbl 1052.37042

[19] —, « $ℝ$eal laminations and the topological dynamics of complex polynomials », Adv. Math. 184 (2004), p. 207–267. MR 2054016

[20] —, « Combinatorial continuity in complex polynomial dynamics », Proc. London Math. Soc. 91 (2005), p. 215–248. Zbl 1077.37038 | MR 2149856

[21] —, « Puiseux series polynomial dynamics and iteration of complex cubic polynomials », Ann. Inst. Fourier (Grenoble) 56 (2006), p. 1337–1404. Numdam | Zbl 1110.37036 | | MR 2273859

[22] J. Luo« Combinatorics and holomorphic dynamics: Captures, matings and Newton’s method », Thèse, Cornell University, 1995. MR 2691795

[23] M. Lyubich« Dynamics of quadratic polynomials. III. Parapuzzle and SBR measures », Astérisque 261 (2000), p. 173–200. Zbl 1044.37038 | MR 1755441

[24] J. Milnor« Geometry and dynamics of quadratic rational maps », Experiment. Math. 2 (1993), p. 37–83. Zbl 0922.58062 | MR 1246482

[25] —, « Rational maps with two critical points », Exper. Math. 9 (2000), p. 481–522. Zbl 0972.30013 | MR 1806289

[26] Y. Minsky« The classification of Kleinian surface groups I », Ann. of Math. 171 (2010), p. 1–107. Zbl 1193.30063 | MR 2630036

[27] C. L. Petersen« Puzzles and Siegel disks », in Progress in holomorphic dynamics, Pitman Res. Notes Math. Ser., vol. 387, Longman, 1998, p. 50–85. Zbl 0948.30027 | MR 1643015

[28] M. Rees« Components of degree two hyperbolic rational maps », Invent. Math. 100 (1990), p. 357–382. Zbl 0712.30022 | | MR 1047139

[29] —, « A partial description of parameter space of rational maps of degree two. I », Acta Math. 168 (1992), p. 11–87. Zbl 0774.58035 | MR 1149864

[30] —, « A partial description of the parameter space of rational maps of degree two. II », Proc. London Math. Soc. 70 (1995), p. 644–690. Zbl 0827.58048 | MR 1317518

[31] —, « Views of parameter space: Topographer and Resident », Astérisque 288 (2003). Zbl 1054.37020

[32] —, « Multiple equivalent matings with the aeroplane polynomial », Ergod. Th. and Dynam. Syst. 30 (2010), p. 1239–1257, with erratum on p. 1259. Zbl 1291.37069 | MR 2669420

[33] —, « The ending laminations theorem direct from teichmuller geodesics », preprint arXiv:math/0404007.

[34] P. Roesch« Puzzles de Yoccoz pour les applications à allure rationnelle », Enseign. Math. 45 (1999), p. 133–168. Zbl 0977.37023 | MR 1703365

[35] —, « Holomorphic motions and puzzles (following m. shishikura) », in The Mandelbrot set, theme and variations, London Math. Soc. Lecture Note Ser., vol. 274, Cambridge Univ. Press, 2000, p. 117–131. Zbl 1063.37042 | MR 1765086

[36] —, « On local connectivity for the julia set of rational maps: Newton’s famous example », Ann. of Math. 168 (2008), p. 127–174. Zbl 1180.30033

[37] J. Stimson« Degree two rational maps with a periodic critical point », Thèse, University of Liverpool, 1993.

[38] L. Tan« Matings of quadratic polynomials », Ergodic Theory Dynam. Systems 12 (1992), p. 589–620. Zbl 0756.58024 | MR 1182664

[39] W. P. Thurston« On the geometry and dynamics of iterated rational maps », in Complex dynamics (D. Schleicher & N. Selinger, éds.), A K Peters, 2009, p. 3–137. Zbl 1185.37111 | MR 2508255

[40] V. Timorin« External boundary of ${m}_{2}$ », in Proceedings of the Fields Institute dedicated to the 75th birthday of J. Milnor, Fields Institute Communications, vol. 53, AMS, 2006, p. 225–267. Zbl 1189.37054

[41] —, « Topological regluing of holomorphic functions », Invent. Math. 179 (2010), p. 461–506. Zbl 1211.37058 | MR 2587338

[42] B. Wittner« On the bifurcation loci of rational maps of degree two », Thèse, Cornell University, 1988. MR 2636558