Strong bifurcation loci of full Hausdorff dimension

 Access to full text

1. [1] M. Aspenberg, Rational Misiurewicz maps are rare, Comm. Math. Phys.291 (2009), 645–658. Zbl1185.37103MR2534788
2. [2] M. Aspenberg & J. Graczyk, Dimension and measure for semi-hyperbolic rational maps of degree 2, C. R. Math. Acad. Sci. Paris347 (2009), 395–400. Zbl1215.37030MR2537237
3. [3] G. Bassanelli & F. Berteloot, Bifurcation currents in holomorphic dynamics on ${\mathbb{P}}^k$, J. reine angew. Math. 608 (2007), 201–235. Zbl1136.37025MR2339474
4. [4] G. Bassanelli & F. Berteloot, Lyapunov exponents, bifurcation currents and laminations in bifurcation loci, Math. Ann.345 (2009), 1–23. Zbl1179.37067MR2520048
5. [5] G. Bassanelli & F. Berteloot, Distribution of polynomials with cycles of a given multiplier, Nagoya Math. J.201 (2011), 23–43. Zbl1267.37049MR2772169
6. [6] E. Bedford & B. A. Taylor, The Dirichlet problem for a complex Monge-Ampere equation, Bull. Amer. Math. Soc.82 (1976), 102–104. Zbl0322.31008MR393574
7. [7] L. Bers & H. L. Royden, Holomorphic families of injections, Acta Math.157 (1986), 259–286. Zbl0619.30027MR857675
8. [8] F. Berteloot, C. Dupont & L. Molino, Normalization of bundle holomorphic contractions and applications to dynamics, Ann. Inst. Fourier (Grenoble) 58 (2008), 2137–2168. Zbl1151.37038MR2473632
9. [9] F. Berteloot & V. Mayer, Rudiments de dynamique holomorphe, Cours Spécialisés 7, Soc. Math. France, 2001. Zbl1051.37019MR1973050
10. [10] B. Branner & J. H. Hubbard, The iteration of cubic polynomials. I. The global topology of parameter space, Acta Math. 160 (1988), 143–206. Zbl0668.30008MR945011
11. [11] X. Buff & A. L. Epstein, Bifurcation measure and postcritically finite rational maps, in Complex dynamics : families and friends / edited by Dierk Schleicher, A K Peters, Ltd., 2009, 491–512. Zbl1180.37056MR2508266
12. [12] E. M. Chirka, Complex analytic sets, Mathematics and its Applications (Soviet Series) 46, Kluwer Academic Publishers Group, 1989. Zbl0683.32002MR1111477
13. [13] L. DeMarco, Dynamics of rational maps: a current on the bifurcation locus, Math. Res. Lett.8 (2001), 57–66. Zbl0991.37030MR1825260
14. [14] L. DeMarco, Dynamics of rational maps: Lyapunov exponents, bifurcations, and capacity, Math. Ann.326 (2003), 43–73. Zbl1032.37029MR1981611
15. [15] T.-C. Dinh & N. Sibony, Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mappings, in Holomorphic dynamical systems, Lecture Notes in Math. 1998, Springer, 2010, 165–294. Zbl1218.37055MR2648690
16. [16] R. Dujardin, Approximation des fonctions lisses sur certaines laminations, Indiana Univ. Math. J.55 (2006), 579–592. Zbl1102.53014MR2225446
17. [17] R. Dujardin, Cubic polynomials: a measurable view on parameter space, in Complex dynamics : families and friends / edited by Dierk Schleicher, A K Peters, Ltd., 2009, 451–490. Zbl1180.37058MR2508265
18. [18] R. Dujardin & C. Favre, Distribution of rational maps with a preperiodic critical point, Amer. J. Math.130 (2008), 979–1032. Zbl1246.37071MR2427006
19. [19] R. Mañé, P. Sad & D. P. Sullivan, On the dynamics of rational maps, Ann. Sci. École Norm. Sup.16 (1983), 193–217. Zbl0524.58025MR732343
20. [20] P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Math. 44, Cambridge Univ. Press, 1995. Zbl0819.28004MR1333890
21. [21] C. T. McMullen, Complex dynamics and renormalization, Annals of Math. Studies 135, Princeton Univ. Press, 1994. Zbl0822.30002MR1312365
22. [22] C. T. McMullen, Hausdorff dimension and conformal dynamics. II. Geometrically finite rational maps, Comment. Math. Helv. 75 (2000), 535–593. Zbl0982.37043MR1789177
23. [23] C. T. McMullen, The Mandelbrot set is universal, in The Mandelbrot set, theme and variations, London Math. Soc. Lecture Note Ser. 274, Cambridge Univ. Press, 2000, 1–17. Zbl1062.37042MR1765082
24. [24] C. T. McMullen & D. P. Sullivan, Quasiconformal homeomorphisms and dynamics. III. The Teichmüller space of a holomorphic dynamical system, Adv. Math. 135 (1998), 351–395. Zbl0926.30028MR1620850
25. [25] W. de Melo & S. van Strien, One-dimensional dynamics, Ergebn. Math. Grenzg. 25, Springer, 1993. Zbl0791.58003MR1239171
26. [26] J. Milnor, On Lattès maps, in Dynamics on the Riemann sphere, Eur. Math. Soc., Zürich, 2006, 9–43. Zbl1235.37015MR2348953
27. [27] J. Rivera-Letelier, On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets, Fund. Math.170 (2001), 287–317. Zbl0985.37041MR1880905
28. [28] W. Rudin, Real and complex analysis, third éd., McGraw-Hill Book Co., 1987. Zbl0278.26001MR924157
29. [29] M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets, Ann. of Math.147 (1998), 225–267. Zbl0922.58047MR1626737
30. [30] M. Shishikura & L. Tan, An alternative proof of Mañé’s theorem on non-expanding Julia sets, in The Mandelbrot set, theme and variations, London Math. Soc. Lecture Note Ser. 274, Cambridge Univ. Press, 2000, 265–279. Zbl1062.37046MR1765093
31. [31] N. Sibony, Dynamique des applications rationnelles de ${𝐏}^k$, in Dynamique et géométrie complexes (Lyon, 1997), Panor. & Synthèses 8, Soc. Math. France, 1999. Zbl1020.37026MR1760844
32. [32] J. H. Silverman, The arithmetic of dynamical systems, Graduate Texts in Math. 241, Springer, 2007. Zbl1130.37001MR2316407
33. [33] S. van Strien, Misiurewicz maps unfold generically (even if they are critically non-finite), Fund. Math.163 (2000), 39–54. Zbl0965.37038MR1750334
34. [34] L. Tan, Hausdorff dimension of subsets of the parameter space for families of rational maps. (A generalization of Shishikura’s result), Nonlinearity 11 (1998), 233–246. Zbl1019.37502MR1610752
35. [35] M. Urbański, Rational functions with no recurrent critical points, Ergodic Theory Dynam. Systems14 (1994), 391–414. Zbl0807.58025MR1279476

1. Xavier Buff, Thomas Gauthier, Perturbations of flexible Lattès maps
2. Romain Dujardin, The supports of higher bifurcation currents