Existence of unique SRB-measures is typical for real unicritical polynomial families

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1. [1] Ahlfors L., Lectures on Quasiconformal Mappings, Van Nostrand, Princeton, NJ, 1966. Zbl0138.06002MR200442
2. [2] Avila A., Lyubich M., de Melo W., Regular or stochastic dynamics in real analytic families of unimodal maps, Invent. Math.154 (2003) 451-550. Zbl1050.37018MR2018784
3. [3] Avila A., Moreira C.G., Statistical properties of unimodal maps: The quadratic family, Ann. of Math.161 (2005) 831-881. Zbl1078.37029MR2153401
4. [4] Birkhoff G., Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc.85 (1957) 219-227. Zbl0079.13502MR87058
5. [5] Blokh A., Lyubich M., Measurable dynamics of S-unimodal maps of the interval, Ann. Sci. École Norm. Sup.24 (1991) 737-749. Zbl0790.58024MR1132757
6. [6] Bruin H., Minimal Cantor systems and unimodal maps, J. Difference Eq. Appl.9 (2003) 305-318. Zbl1026.37003MR1990338
7. [7] Bruin H., Topological conditions for the existence of Cantor attractors, Trans. Amer. Math. Soc.350 (1998) 2229-2263. Zbl0901.58029MR1458316
8. [8] Bruin H., Luzzatto S., van Strien S., Decay of correlations in one-dimensional dynamics, Ann. Sci. École Norm. Sup.36 (2003) 621-646. Zbl1039.37021MR2013929
9. [9] Bruin H., Keller G., Nowicki T., van Strien S., Wild Cantor attractors exist, Ann. of Math.143 (1996) 97-130. Zbl0848.58016MR1370759
10. [10] Bruin H., Shen W., van Strien S., Invariant measures exist without a growth condition, Commun. Math. Phys.241 (2–3) (2003) 287-306. Zbl1098.37034MR2013801
11. [11] Douady A., Hubbard J., Dynamical study of complex polynomials, Part I and Part II, Mathematical Publications of Orsay 84-2, 85-4 (in French). 
12. [12] Douady A., Hubbard J., On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. (4)18 (2) (1985) 287-343. Zbl0587.30028MR816367
13. [13] Durand F., Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynam. Syst.20 (2000) 1061-1078. Zbl0965.37013MR1779393
14. [14] Graczyk J., Świa̧tek G., Induced expansion for quadratic polynomials, Ann. Sci École Norm. Súp.29 (1996) 399-482. Zbl0867.58048
15. [15] Hasselblatt B., Katok A., A First Course in Dynamics, with a Panorama of Recent Developments, Cambridge University Press, Cambridge, 2003. Zbl1027.37001MR1995704
16. [16] Hofbauer F., Keller G., Some remarks on recent results about S-unimodal maps, Ann. Inst. Henri Poincaré53 (1990) 413-425. Zbl0721.58018MR1096100
17. [17] Kahn J., Holomorphic removability of Julia sets, IMS preprint ims98-11. 
18. [18] Kozlovski O., Getting rid of the negative Schwarzian derivative condition, Ann. of Math.152 (2000) 743-762. Zbl0988.37044MR1815700
19. [19] Kozlovski O., Shen W., van Strien S., Rigidity for real polynomials, Ann. of Math., in press. Zbl1129.37020
20. [20] Kozlovski O., Shen W., van Strien S., Density of Axiom A in dimension one, Ann. of Math., in press. Zbl1138.37013
21. [21] Lyubich M., Combinatorics, geometry and attractors of quasi-quadratic maps, Ann. of Math.140 (1994) 347-404, and Erratum Manuscript (2000). Zbl0821.58014MR1298717
22. [22] Lyubich M., Dynamics of quadratic polynomials. III. Parapuzzle and SRB measures, in: Géométrie complexe et systèmes dynamiques, Orsay, 1995, Astérisque, vol. 261, 2000, pp. xii-xiii, 173–200. Zbl1044.37038MR1755441
23. [23] Lyubich M., Feigenbaum–Coullet–Tresser universality and Milnor's hairiness conjecture, Ann. of Math.149 (2) (1999) 319-420. Zbl0945.37012MR1689333
24. [24] Lyubich M., Almost every real quadratic map is either regular or stochastic, Ann. of Math.156 (2002) 1-78. Zbl1160.37356MR1935840
25. [25] McMullen C., Complex Dynamics and Renormalization, Ann. of Math Stud., vol. 135, 1994. Zbl0822.30002MR1312365
26. [26] Mañé R., Ergodic Theory and Differentiable Dynamics, Springer, New York, 1987. Zbl0616.28007MR889254
27. [27] Martens M., Distortion results and invariant Cantor sets of unimodal maps, Ergodic Theory Dynam. Syst.14 (2) (1994) 331-349. Zbl0809.58026MR1279474
28. [28] Martens M., Nowicki T., Invariant measures for typical quadratic maps, in: Géométrie complexe et systèmes dynamiques, Orsay, 1995, Astérisque, vol. 261, 2000, pp. 239-252. Zbl0939.37020MR1755443
29. [29] de Melo W., van Strien S., One-Dimensional Dynamics, Springer, Berlin, 1993. Zbl0791.58003MR1239171
30. [30] Milnor J., Periodic orbits, externals rays and the Mandelbrot set: An expository account, in: Géométrie complexe et systèmes dynamiques, Orsay, 1995, Astérisque, vol. 261, 2000, pp. xiii, 277–333. Zbl0941.30016MR1755445
31. [31] Nowicki T., van Strien S., Invariant measures exist under a summability condition, Invent. Math.105 (1991) 123-136. Zbl0736.58030MR1109621
32. [32] Rivera-Letelier J., Rational maps with decay of geometry: Rigidity, Thurston's algorithm and local connectivity, IMS preprint ims00-09. 
33. [33] Roesch P., Holomorphic motions and puzzles (following M. Shishikura), in: The Mandelbrot set theme and variations, London Math. Soc. Lecture Note Ser., vol. 274, Cambridge University Press, Cambridge, 2000, pp. 117-131. Zbl1063.37042MR1765086
34. [34] Shen W., Bounds for one-dimensional maps without inflection critical points, J. Math. Sci. Univ. Tokyo10 (1) (2003) 41-88. Zbl1184.37035MR1963798
35. [35] Shen W., Decay geometry for unimodal maps: an elementary proof, Ann. of Math. (2)163 (2) (2006) 383-404. Zbl1097.37032MR2199221
36. [36] Shishikura M., Yoccoz puzzles, τ-functions and their applications, Unpublished. 
37. [37] Slodkowski Z., Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc.111 (2) (1991) 347-355. Zbl0741.32009MR1037218
38. [38] van Strien S., Vargas E., Real bounds, ergodicity and negative Schwarzian for multimodal maps, J. Amer. Math. Soc.17 (2004) 749-782. Zbl1073.37043MR2083467
39. [39] Yoccoz J.-C., Unpublished.