@article{ASENS_2007_4_40_1_135_0, author = {Przytycki, Feliks and Rivera-Letelier, Juan}, title = {Statistical properties of topological Collet-Eckmann maps}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {40}, year = {2007}, pages = {135-178}, doi = {10.1016/j.ansens.2006.11.002}, zbl = {1115.37048}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_1_135_0} }
Przytycki, Feliks; Rivera-Letelier, Juan. Statistical properties of topological Collet-Eckmann maps. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 135-178. doi : 10.1016/j.ansens.2006.11.002. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_1_135_0/
[1] Aspenberg M., The Collet-Eckmann condition for rational functions on the Riemann sphere, Ph.D. Thesis, KTH, Sweden, 2004.
[2] Iteration of Rational Functions. Complex Analytic Dynamical Systems, Graduate Texts in Mathematics, vol. 132, Springer-Verlag, New York, 1991. | MR 1128089 | Zbl 1120.30300
,[3] Bernard J., Dynamique des perturbations d'un exemple de Lattès, Ph.D. Thesis, Université de Paris-Sud, 1994.
[4] Equilibrium states for S-unimodal maps, Ergodic Theory Dynam. Systems 18 (1998) 765-789. | MR 1645373 | Zbl 0916.58020
, ,[5] Decay of correlations in one-dimensional dynamics, Ann. Sci. École Norm. Sup. 36 (2003) 621-646. | Numdam | MR 2013929 | Zbl 1039.37021
, , ,[6] Complex maps without invariant densities, Nonlinearity 19 (2006) 2929-2945. | MR 2275506 | Zbl 1122.37037
, ,[7] Complex Dynamics, Springer-Verlag, Berlin/New York, 1993. | MR 1230383 | Zbl 0782.30022
, ,[8] Positive Liapunov exponents and absolute continuity for maps of the interval, Ergodic Theory Dynam. Systems 3 (1983) 13-46. | MR 743027 | Zbl 0532.28014
, ,[9] Conformal measures for rational functions revisited, Fund. Math. 157 (1998) 161-173. | MR 1636885 | Zbl 0915.58041
, , , ,[10] On the transfer operator for rational functions on the Riemann sphere, Ergodic Theory Dynam. Systems 16 (1996) 255-266. | MR 1389624 | Zbl 0852.46024
, , ,[11] On Sullivan's conformal measures for rational maps of the Riemann sphere, Nonlinearity 4 (1991) 365-384. | MR 1107011 | Zbl 0722.58028
, ,[12] On thermodynamics of rational maps on the Riemann sphere, http://www.arxiv.org/math.DS/0603507. | MR 2342967
, , ,[13] Dobbs N., Critical points, cusps and induced expansion, Doctoral Thesis, Université Paris-Sud (Orsay), 2006.
[14] Distribution of rational maps with a preperiodic critical point, http://www.arxiv.org/math.DS/0601612.
, ,[15] Gouëzel S., Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes, Ph.D. Thesis, Université de Paris-Sud, 2004.
[16] Collet, Eckmann and Hölder, Invent. Math. 133 (1998) 69-96. | MR 1626469 | Zbl 0916.30023
, ,[17] Graczyk J., Smirnov S., Weak expansion and geometry of Julia sets, to appear in Invent. Math. A preprint version: March 1999.
[18] Harmonic measure and expansion on the boundary of the connectedness locus, Invent. Math. 142 (2000) 605-629. | Zbl 1052.37041
, ,[19] Convergence of the transfer operator for rational maps, Ergodic Theory Dynam. Systems 19 (1999) 657-669. | MR 1695914 | Zbl 0953.37006
,[20] Some properties of absolutely continuous invariant measures on an interval, Ergodic Theory Dynam. Systems 1 (1981) 77-93. | MR 627788 | Zbl 0487.28015
,[21] Quelques propriétés ergodiques des applications rationnelles, C. R. Acad. Sci. Paris 299 (1984) 37-40. | MR 756305 | Zbl 0567.58016
,[22] Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps, Comm. Math. Phys. 149 (1992) 31-69. | Zbl 0763.58024
, ,[23] The Hausdorff dimension of invariant probabilities of rational maps, in: Dynamical Systems, Valparaiso, 1986, Lecture Notes in Math., vol. 1331, Springer-Verlag, Berlin, 1988, pp. 86-117. | MR 961095 | Zbl 0658.58015
,[24] Distortion results and invariant Cantor sets of unimodal mappings, Ergodic Theory Dynam. Systems 14 (1994) 331-349. | MR 1279474 | Zbl 0809.58026
,[25] Hausdorff dimension and conformal dynamics. II. Geometrically finite rational maps, Comment. Math. Helv. 75 (2000) 535-593. | MR 1789177 | Zbl 0982.37043
,[26] Graph Directed Markov Systems. Geometry and Dynamics of Limit Sets, Cambridge Tracts in Mathematics, vol. 148, Cambridge Univ. Press, Cambridge, 2003. | MR 2003772 | Zbl 1033.37025
, ,[27] Dynamics in One Complex Variable. Introductory Lectures, Friedr. Vieweg & Sohn, Braunschweig, 1999. | MR 1721240 | Zbl 0946.30013
,[28] Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math. 132 (1998) 633-680. | MR 1625708 | Zbl 0908.58016
, ,[29] Equilibrium measures for some one dimensional maps, Mosc. Math. J. 5 (2005) 669-678. | MR 2241816 | Zbl 1109.37028
, ,[30] Lyapunov characteristic exponents are nonnegative, Proc. Amer. Math. Soc. 119 (1993) 309-317. | MR 1186141 | Zbl 0787.58037
,[31] On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps, in: , , (Eds.), Int. Conf. on Dynamical Systems-a tribute to R. Mañé, Montevideo, 1995, Pitman Res. Notes in Math. Series, vol. 362, Longman, Harlow, 1996, pp. 167-181. | Zbl 0868.58063
,[32] Iterations of holomorphic Collet-Eckmann maps: Conformal and invariant measures, Trans. Amer. Math. Soc. 350 (1998) 717-742. | Zbl 0892.58063
,[33] Hölder implies CE, Astérisque 261 (2000) 385-403. | MR 1755448 | Zbl 0939.37026
,[34] Conical limit set and Poincaré exponent for iterations of rational functions, Trans. Amer. Math. Soc. 351 (1999) 2081-2099. | MR 1615954 | Zbl 0920.58037
,[35] Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps, Invent. Math. 151 (2003) 29-63. | MR 1943741 | Zbl 1038.37035
, , ,[36] Rigidity of holomorphic Collet-Eckmann repellers, Ark. Mat. 37 (1999) 357-371. | Zbl 1034.37026
, ,[37] Fractals in the Plane, Ergodic Theory Methods, Cambridge Univ. Press, in press. Available on, http://www.math.unt.edu/~urbanski.
, ,[38] Measures and dimensions in conformal dynamics, Bull. Amer. Math. Soc. 40 (2003) 281-321. | MR 1978566 | Zbl 1031.37041
,[39] Positive measure sets of ergodic rational maps, Ann. Sci. École Norm. Sup. 19 (1986) 383-407. | Numdam | MR 870689 | Zbl 0611.58038
,[40] A connecting lemma for rational maps satisfying a no-growth condition, Ergodic Theory Dynam. Systems 27 (2007) 595-636. | MR 2308147 | Zbl 1110.37037
,[41] Dimension of weakly expanding points for quadratic maps, Bull. Soc. Math. France 131 (2003) 399-420. | Numdam | MR 2017145 | Zbl 1071.37028
,[42] Symbolic dynamics and Collet-Eckmann condition, Internat. Math. Res. Notices 7 (2000) 333-351. | Zbl 0983.37052
,[43] Conformal dynamical systems, in: Geometric Dynamics, Rio de Janeiro, 1981, Lecture Notes in Math., vol. 1007, Springer-Verlag, Berlin, 1983, pp. 725-752. | MR 730296 | Zbl 0524.58024
,[44] Measures and dimensions in conformal dynamics, Bull. Amer. Math. Soc. 40 (2003) 281-321. | MR 1978566 | Zbl 1031.37041
,[45] Decay of correlations for certain quadratic maps, Comm. Math. Phys. 146 (1992) 123-138. | MR 1163671 | Zbl 0760.58030
,[46] Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | MR 1750438 | Zbl 0983.37005
,[47] Parabolic orbifolds and the dimension of the maximal measure for rational maps, Invent. Math. 99 (1990) 627-649. | MR 1032883 | Zbl 0820.58038
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