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Forty years of unimodal dynamics: On the occasion of Artur Avila winning the Brin Prize
1.  Mathematics Department, Stony Brook University, Stony Brook, NY, 117943651, USA Government 
References:
[1] 
A. Avila and M. Lyubich, Examples of Feigenbaum Julia sets with small Hausdorff dimension,, in, (2006), 71. 
[2] 
A. Avila and M. Lyubich, Hausdorff dimension and conformal measures of Feigenbaum Julia sets,, J. of the AMS, 21 (2008), 305. 
[3] 
A. Avila and M. Lyubich, The full renormalization horseshoe for unimodal maps of higher degree: Exponential contraction along hybrid classes,, Publ. Math. IHÉS, 114 (2011), 171. 
[4] 
A. Avila and M. Lyubich, Feigenbaum Julia sets of positive area,, Manuscript, (2011). 
[5] 
A. Avila, M. Lyubich and W. de Melo, Regular or stochastic dynamics in real analytic families of unimodal maps,, Invent. Math., 154 (2003), 451. doi: 10.1007/s0022200303076. 
[6] 
A. Avila, J. Kahn, M. Lyubich and W. Shen, Combinatorial rigidity for unicritical polynomials,, Annals of Math. (2), 170 (2009), 783. doi: 10.4007/annals.2009.170.783. 
[7] 
A. Avila, M. Lyubich and W. Shen, Parapuzzle of the Multibrot set and typical dynamics of unimodal maps,, J. of European Math. Soc., 13 (2011), 27. doi: 10.4171/JEMS/243. 
[8] 
A. Avila and C. G. Moreira, Statistical properties ofunimodal maps: The quadratic family,, Annals of Math. (2), 161 (2005), 831. 
[9] 
A. Avila and C. G. Moreira, Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative,, in, 286 (2003), 81. 
[10] 
A. Avila and C. G. Moreira, Statistical properties of unimodal maps: Physical measures, periodic orbits and pathological laminations,, Publications Math. IHÉS, 101 (2005), 1. 
[11] 
A. Avila and C. G. Moreira, Hausdorff dimension and the quadratic family,, Manuscript, (2002). 
[12] 
M. Benedicks and L. Carleson, On iterations of $1ax^2$ on (1,1),, Annals of Math. (2), 122 (1985), 1. doi: 10.2307/1971367. 
[13] 
M. Benedicks and L. Carleson, The dynamics of the Hénon map,, Annals of Math. (2), 133 (1991), 73. doi: 10.2307/2944326. 
[14] 
X. Buff and A. Cheritat, Quadratic Julia sets with positive area (2008),, , (). 
[15] 
B. Branner and J. Hubbard, The iteration of cubic polynomials. II. Patterns and parapatterns,, Acta Math., 169 (1992), 229. 
[16] 
R. Brooks and J. Matelski, The dynamics of 2generator subgroups of $\PSL(2, \C)$,, in, (1978), 65. 
[17] 
A. Blokh and M. Lyubich, Measurable dynamics of $S$unimodal maps of the interval,, Ann. Sci. Éc. Norm Sup. (4), 24 (1991), 545. 
[18] 
H. Bruin, G. Keller, T. Nowicki and S. van Strien, Wild Cantor attractors exist,, Annals of Math. (2), 143 (1996), 97. doi: 10.2307/2118654. 
[19] 
H. Bruin, W. Shen and S. van Strien, Existence of unique SRBmeasures is typical for real unicritical polynomial families,, Ann. Sci. Éc. Norm. Sup. (4), 39 (2006), 381. 
[20] 
L. Carleson and T. Gamelin, "Complex Dynamics,", Universitext: Tracts in Mathematics, (1993). 
[21] 
T. Clark, "Real and Complex Dynamics of Unicritical Maps,", Ph.D. Thesis,, University of Toronto, (2010). 
[22] 
P. Collet and J.P. Eckmann, "Iterated Maps of the Interval as Dynamical Systems,", Progress in Physics, 1 (1980). 
[23] 
P. Collet and J.P. Eckmann, Positive Liapunov exponents and absolute continuity for maps of the interval,, Erg. Th. and Dyn Syst., 3 (1983), 13. 
[24] 
D. Cheragni, "Dynamics of Complex Unicritical Polynomials,", Ph.D. Thesis, (2009). 
[25] 
A. Douady, Description of compact sets in $\C$,, in, (1993), 429. 
[26] 
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes,, preprint, (): 84. 
[27] 
A. Douady and J. H. Hubbard, On the dynamics of polynomiallike maps,, Ann. Sc. Éc. Norm. Sup. (4), 18 (1985), 287. 
[28] 
H. Epstein, Fixed points of the perioddoubling operator,, Lecture notes, (1992). 
[29] 
E. de Faria, W. de Melo and A. Pinto, Global hyperbolicity of renormalization for $C^r$ unimodal mappings,, Annals of Math. (2), 164 (2006), 731. doi: 10.4007/annals.2006.164.731. 
[30] 
J. Guckenheimer, Sensitive dependence to initial conditions for onedimensional maps,, Comm. Math. Physics., 70 (1979), 133. doi: 10.1007/BF01982351. 
[31] 
J. Graczyk and G. Światek, Generic hyperbolicity in the logistic family,, Annals of Math. (2), 146 (1997), 1. 
[32] 
H. Inou and M. Shishikura, The renormalization for parabolic fixed points and their perturbations,, Manuscript, (2006). 
[33] 
J. H. Hubbard, Local connectivity of Julia sets and bifurcation loci: Three theorems of J.C. Yoccoz,, in, (1993), 467. 
[34] 
J. Hu and Y. Jiang, The Julia set of the Feigenbaum quadratic polynomial is locally connected,, Manuscript, (1993). 
[35] 
F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure,, Comm. Math. Phys., 127 (1990), 319. 
[36] 
M. Jakobson, Absolutely continuous invariant measures for oneparameter families of onedimensional maps,, Comm. Math. Phys., 81 (1981), 39. doi: 10.1007/BF01941800. 
[37] 
S. Johnson, Singular measures without restrictive intervals,, Comm. Math. Phys., 110 (1987), 185. doi: 10.1007/BF01207362. 
[38] 
L. Jonker and D. Rand, Bifurcations in one dimension. I. The nonwandering set,, Inventiones Math., 62 (1981), 347. 
[39] 
J. Kahn, A priori bounds for some infinitely renormalizable quadratics. I. Bounded primitive combinatorics,, preprint, (2006). 
[40] 
J. Kahn and M. Lyubich, The quasiadditivity Law in conformal geometry,, Annals of Math. (2), 169 (2009), 561. doi: 10.4007/annals.2009.169.561. 
[41] 
J. Kahn and M. Lyubich, Local connectivity of Julia sets for unictritical polynomials,, Annals of Math. (2), 170 (2009), 413. doi: 10.4007/annals.2009.170.783. 
[42] 
J. Kahn and M. Lyubich, A priori bounds for some infinitely renormalizable quadratics. II. Decorations,, Annals Sci. École Norm. Sup. (4), 41 (2008), 57. 
[43] 
O. Kozlovski, Axiom A maps are dense in the space of unimodal maps in the $C^k$ topology,, Annals of Math. (2), 157 (2003), 1. doi: 10.4007/annals.2003.157.1. 
[44] 
O. Kozlovski, W. Shen and S. van Strien, Rigidity for real polynomials,, Annals of Math. (2), 165 (2007), 749. doi: 10.4007/annals.2007.165.749. 
[45] 
O. Kozlovski, W. Shen and S. van Strien, Density of hyperbolicity in dimension one,, Annals of Math. (2), 166 (2007), 145. doi: 10.4007/annals.2007.166.145. 
[46] 
G. Levin and S. van Strien, Local connectivity of the Julia set of real polynomials,, Annals of Math. (2), 147 (1998), 471. doi: 10.2307/120958. 
[47] 
O. E. Lanford III, A computer assisted proof of the Feigenbaum conjectures,, Bull. Amer. Math. Soc. (N.S.), 6 (1982), 427. 
[48] 
F. Ledrappier, Some properties of an absolutely continuous invariant measure on an interval,, Erg. Th. and Dyn. Syst., 1 (1981), 77. 
[49] 
Y. Lyubich, "Introduction to the Theory of Banach Representations of Groups,", Birkhäuser, (1988). 
[50] 
M. Lyubich, On the Lebesgue measure of the Julia set of a quadratic polynomial,, preprint, (1991). 
[51] 
M. Lyubich, Combinatorics, geometry and attractors of quasiquadratic maps,, Annals of Math. (2), 140 (1994), 347. doi: 10.2307/2118604. 
[52] 
M. Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math.,, 178 (1997), 178 (1997), 185. 
[53] 
M. Lyubich, How big is the set of infinitely renormalizable quadratics?,, in, 184 (1998), 131. 
[54] 
M. Lyubich, Dynamics of quadratic polynomials. III. Parapuzzle and SBR measures,, Astérisque, 261 (2000), 173. 
[55] 
M. Lyubich, FeigenbaumCoulletTresser universality and Milnor's hairiness conjecture,, Annals of Math. (2), 149 (1999), 319. doi: 10.2307/120968. 
[56] 
M. Lyubich, Almost every real quadratic map is either regular or stochastic,, Annals of Math. (2), 156 (2002), 1. doi: 10.2307/3597183. 
[57] 
M. Lyubich and J. Milnor, The Fibonacci unimodal map,, Journal of AMS, 6 (1993), 425. 
[58] 
M. Lyubich and M. Yampolsky, Dynamics of quadratic polynomials: Complex bounds for real maps,, Ann. Inst. Fourier (Grenoble), 47 (1997), 1219. doi: 10.5802/aif.1598. 
[59] 
T. Y. Li and J. Yorke, Period three implies chaos,, Amer. Math. Monthly, 82 (1975), 985. doi: 10.2307/2318254. 
[60] 
M. Martens, Distortion results and invariant Cantor sets of unimodal maps,, Erg. Th. & Dyn. Syst., 14 (1994), 331. 
[61] 
M. Martens, The periodic points of renormalization,, Ann. Math., 147 (1998), 543. doi: 10.2307/120959. 
[62] 
M. Martens and T. Nowicki, Invariant measures for Lebesgue typical quadratic maps,, Astérisque, 261 (2000), 239. 
[63] 
M. Martens and W. de Melo, The multipliers of periodic points in onedimensional dynamics,, Nonlinearity, 12 (1999), 217. doi: 10.1088/09517715/12/2/003. 
[64] 
R. M. May, Simple mathematical models with very complicated dynamics,, Nature, 261 (1976), 459. doi: 10.1038/261459a0. 
[65] 
C. McMullen, "Complex Dynamics and Renormalization,", Princeton University Press, (1994). 
[66] 
C. McMullen, "Renormalization and Three Manifolds which Fiber Over the Circle,", Princeton University Press, (1996). 
[67] 
C. McMullen, Selfsimilarity of Siegel disks and Hausdorff dimension of Julia sets,, Acta Math., 180 (1998), 247. doi: 10.1007/BF02392901. 
[68] 
M. Misiurewicz, Absolutely continuous measures for certain maps of an interval,, IHÉS Publ. Math., 53 (1981), 17. 
[69] 
M. Metropolis, M. Stein and P. Stein, On finite limit sets for transformations on the unit interval,, J. Combinatorial Theory Ser. A, 15 (1973), 25. doi: 10.1016/00973165(73)900332. 
[70] 
W. de Melo and S. van Strien, "OneDimensional Dynamics,", Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 25 (1993). 
[71] 
J. Milnor, "Dynamics in One Complex Variable,", Third edition, 160 (2006). 
[72] 
J. Milnor, On the concept of attractor,, Comm. Math. Physics, 99 (1985), 177. doi: 10.1007/BF01212280. 
[73] 
J. Milnor, Local connectivity of Julia sets: Expository lectures,, in, 274 (2000), 67. 
[74] 
J. Milnor, Fubini foiled: Katok's paradoxical example in measure theory,, Math. Intell., 19 (1997), 30. doi: 10.1007/BF03024428. 
[75] 
J. Milnor and W. Thurston, On iterated maps of the interval,, in, 1342 (1988), 1986. 
[76] 
P. J. Myrberg, Sur l'itération des polynomes réels quadratiques,, J. Math. Pures Appl. (9), 41 (1962), 339. 
[77] 
T. Nowicki and S. van Strien, Absolutely continuous measures for c^{2} unimodal maps satisfying the ColletEckmann conditions,, Invent. Math., 93 (1988), 619. doi: 10.1007/BF01410202. 
[78] 
J. Palis, A global view of dynamics and a Conjecture of the denseness of finitude of attractors,, Astérique, 261 (2000), 335. 
[79] 
E. A. Prado, Ergodicity of conformal measures for unimodal polynomials,, Conform. Geom. Dyn., 2 (1998), 29. 
[80] 
F. Przytycki and S. Rhode, Porosity of ColletEckmann Julia sets,, Fund. Math., 155 (1998), 189. 
[81] 
D. Sullivan, Quasiconformal homeomorphisms and dynamics, topology, and geometry,, in, (1986), 1216. 
[82] 
D. Sullivan, Bounds, quadratic differentials, and renormalization conjetures,, in, (1988). 
[83] 
W. Shen, Decay of geometry for unimodal maps: An elementary proof,, Annals of Math. (2), 163 (2006), 383. doi: 10.4007/annals.2006.163.383. 
[84] 
D. Smania, On the hyperbolicity of the perioddoubling fixed point,, Trans. AMS, 358 (2006), 1827. 
[85] 
M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets,, Annals of Math. (2), 147 (1998), 225. doi: 10.2307/121009. 
[86] 
M. Shishikura, Topological, geometric and complex analytic properties of Julia sets,, in, (1995), 886. 
[87] 
M. Shub and A. Wilkinson, Pathological foliations and removable zero exponents,, Invetiones Math., 139 (2000), 495. doi: 10.1007/s002229900035. 
[88] 
W. Thurston, On the geometry and dynamics of iterated rational maps,, in, (2009), 3. 
[89] 
E. B. Vul, Y. G. Sinaĭ and K. M. Khanin, Feigenbaum universality and the thermodynamical formalism,, Russian Math. Surveys, 39 (1984), 1. 
[90] 
M. Yampolsky, Siegel disks and renormalization fixed points,, in, 53 (2008), 377. 
[91] 
B. Yarrington, "Local Connectivity and Lebesgue Measure of Polynomial Julia Sets,", Ph.D. Thesis, (1995). 
[92] 
L.S. Young, Decay of correlations for certain quadratic maps,, Comm. Math. Phys., 146 (1992), 123. doi: 10.1007/BF02099211. 
show all references
References:
[1] 
A. Avila and M. Lyubich, Examples of Feigenbaum Julia sets with small Hausdorff dimension,, in, (2006), 71. 
[2] 
A. Avila and M. Lyubich, Hausdorff dimension and conformal measures of Feigenbaum Julia sets,, J. of the AMS, 21 (2008), 305. 
[3] 
A. Avila and M. Lyubich, The full renormalization horseshoe for unimodal maps of higher degree: Exponential contraction along hybrid classes,, Publ. Math. IHÉS, 114 (2011), 171. 
[4] 
A. Avila and M. Lyubich, Feigenbaum Julia sets of positive area,, Manuscript, (2011). 
[5] 
A. Avila, M. Lyubich and W. de Melo, Regular or stochastic dynamics in real analytic families of unimodal maps,, Invent. Math., 154 (2003), 451. doi: 10.1007/s0022200303076. 
[6] 
A. Avila, J. Kahn, M. Lyubich and W. Shen, Combinatorial rigidity for unicritical polynomials,, Annals of Math. (2), 170 (2009), 783. doi: 10.4007/annals.2009.170.783. 
[7] 
A. Avila, M. Lyubich and W. Shen, Parapuzzle of the Multibrot set and typical dynamics of unimodal maps,, J. of European Math. Soc., 13 (2011), 27. doi: 10.4171/JEMS/243. 
[8] 
A. Avila and C. G. Moreira, Statistical properties ofunimodal maps: The quadratic family,, Annals of Math. (2), 161 (2005), 831. 
[9] 
A. Avila and C. G. Moreira, Statistical properties of unimodal maps: Smooth families with negative Schwarzian derivative,, in, 286 (2003), 81. 
[10] 
A. Avila and C. G. Moreira, Statistical properties of unimodal maps: Physical measures, periodic orbits and pathological laminations,, Publications Math. IHÉS, 101 (2005), 1. 
[11] 
A. Avila and C. G. Moreira, Hausdorff dimension and the quadratic family,, Manuscript, (2002). 
[12] 
M. Benedicks and L. Carleson, On iterations of $1ax^2$ on (1,1),, Annals of Math. (2), 122 (1985), 1. doi: 10.2307/1971367. 
[13] 
M. Benedicks and L. Carleson, The dynamics of the Hénon map,, Annals of Math. (2), 133 (1991), 73. doi: 10.2307/2944326. 
[14] 
X. Buff and A. Cheritat, Quadratic Julia sets with positive area (2008),, , (). 
[15] 
B. Branner and J. Hubbard, The iteration of cubic polynomials. II. Patterns and parapatterns,, Acta Math., 169 (1992), 229. 
[16] 
R. Brooks and J. Matelski, The dynamics of 2generator subgroups of $\PSL(2, \C)$,, in, (1978), 65. 
[17] 
A. Blokh and M. Lyubich, Measurable dynamics of $S$unimodal maps of the interval,, Ann. Sci. Éc. Norm Sup. (4), 24 (1991), 545. 
[18] 
H. Bruin, G. Keller, T. Nowicki and S. van Strien, Wild Cantor attractors exist,, Annals of Math. (2), 143 (1996), 97. doi: 10.2307/2118654. 
[19] 
H. Bruin, W. Shen and S. van Strien, Existence of unique SRBmeasures is typical for real unicritical polynomial families,, Ann. Sci. Éc. Norm. Sup. (4), 39 (2006), 381. 
[20] 
L. Carleson and T. Gamelin, "Complex Dynamics,", Universitext: Tracts in Mathematics, (1993). 
[21] 
T. Clark, "Real and Complex Dynamics of Unicritical Maps,", Ph.D. Thesis,, University of Toronto, (2010). 
[22] 
P. Collet and J.P. Eckmann, "Iterated Maps of the Interval as Dynamical Systems,", Progress in Physics, 1 (1980). 
[23] 
P. Collet and J.P. Eckmann, Positive Liapunov exponents and absolute continuity for maps of the interval,, Erg. Th. and Dyn Syst., 3 (1983), 13. 
[24] 
D. Cheragni, "Dynamics of Complex Unicritical Polynomials,", Ph.D. Thesis, (2009). 
[25] 
A. Douady, Description of compact sets in $\C$,, in, (1993), 429. 
[26] 
A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes,, preprint, (): 84. 
[27] 
A. Douady and J. H. Hubbard, On the dynamics of polynomiallike maps,, Ann. Sc. Éc. Norm. Sup. (4), 18 (1985), 287. 
[28] 
H. Epstein, Fixed points of the perioddoubling operator,, Lecture notes, (1992). 
[29] 
E. de Faria, W. de Melo and A. Pinto, Global hyperbolicity of renormalization for $C^r$ unimodal mappings,, Annals of Math. (2), 164 (2006), 731. doi: 10.4007/annals.2006.164.731. 
[30] 
J. Guckenheimer, Sensitive dependence to initial conditions for onedimensional maps,, Comm. Math. Physics., 70 (1979), 133. doi: 10.1007/BF01982351. 
[31] 
J. Graczyk and G. Światek, Generic hyperbolicity in the logistic family,, Annals of Math. (2), 146 (1997), 1. 
[32] 
H. Inou and M. Shishikura, The renormalization for parabolic fixed points and their perturbations,, Manuscript, (2006). 
[33] 
J. H. Hubbard, Local connectivity of Julia sets and bifurcation loci: Three theorems of J.C. Yoccoz,, in, (1993), 467. 
[34] 
J. Hu and Y. Jiang, The Julia set of the Feigenbaum quadratic polynomial is locally connected,, Manuscript, (1993). 
[35] 
F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure,, Comm. Math. Phys., 127 (1990), 319. 
[36] 
M. Jakobson, Absolutely continuous invariant measures for oneparameter families of onedimensional maps,, Comm. Math. Phys., 81 (1981), 39. doi: 10.1007/BF01941800. 
[37] 
S. Johnson, Singular measures without restrictive intervals,, Comm. Math. Phys., 110 (1987), 185. doi: 10.1007/BF01207362. 
[38] 
L. Jonker and D. Rand, Bifurcations in one dimension. I. The nonwandering set,, Inventiones Math., 62 (1981), 347. 
[39] 
J. Kahn, A priori bounds for some infinitely renormalizable quadratics. I. Bounded primitive combinatorics,, preprint, (2006). 
[40] 
J. Kahn and M. Lyubich, The quasiadditivity Law in conformal geometry,, Annals of Math. (2), 169 (2009), 561. doi: 10.4007/annals.2009.169.561. 
[41] 
J. Kahn and M. Lyubich, Local connectivity of Julia sets for unictritical polynomials,, Annals of Math. (2), 170 (2009), 413. doi: 10.4007/annals.2009.170.783. 
[42] 
J. Kahn and M. Lyubich, A priori bounds for some infinitely renormalizable quadratics. II. Decorations,, Annals Sci. École Norm. Sup. (4), 41 (2008), 57. 
[43] 
O. Kozlovski, Axiom A maps are dense in the space of unimodal maps in the $C^k$ topology,, Annals of Math. (2), 157 (2003), 1. doi: 10.4007/annals.2003.157.1. 
[44] 
O. Kozlovski, W. Shen and S. van Strien, Rigidity for real polynomials,, Annals of Math. (2), 165 (2007), 749. doi: 10.4007/annals.2007.165.749. 
[45] 
O. Kozlovski, W. Shen and S. van Strien, Density of hyperbolicity in dimension one,, Annals of Math. (2), 166 (2007), 145. doi: 10.4007/annals.2007.166.145. 
[46] 
G. Levin and S. van Strien, Local connectivity of the Julia set of real polynomials,, Annals of Math. (2), 147 (1998), 471. doi: 10.2307/120958. 
[47] 
O. E. Lanford III, A computer assisted proof of the Feigenbaum conjectures,, Bull. Amer. Math. Soc. (N.S.), 6 (1982), 427. 
[48] 
F. Ledrappier, Some properties of an absolutely continuous invariant measure on an interval,, Erg. Th. and Dyn. Syst., 1 (1981), 77. 
[49] 
Y. Lyubich, "Introduction to the Theory of Banach Representations of Groups,", Birkhäuser, (1988). 
[50] 
M. Lyubich, On the Lebesgue measure of the Julia set of a quadratic polynomial,, preprint, (1991). 
[51] 
M. Lyubich, Combinatorics, geometry and attractors of quasiquadratic maps,, Annals of Math. (2), 140 (1994), 347. doi: 10.2307/2118604. 
[52] 
M. Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math.,, 178 (1997), 178 (1997), 185. 
[53] 
M. Lyubich, How big is the set of infinitely renormalizable quadratics?,, in, 184 (1998), 131. 
[54] 
M. Lyubich, Dynamics of quadratic polynomials. III. Parapuzzle and SBR measures,, Astérisque, 261 (2000), 173. 
[55] 
M. Lyubich, FeigenbaumCoulletTresser universality and Milnor's hairiness conjecture,, Annals of Math. (2), 149 (1999), 319. doi: 10.2307/120968. 
[56] 
M. Lyubich, Almost every real quadratic map is either regular or stochastic,, Annals of Math. (2), 156 (2002), 1. doi: 10.2307/3597183. 
[57] 
M. Lyubich and J. Milnor, The Fibonacci unimodal map,, Journal of AMS, 6 (1993), 425. 
[58] 
M. Lyubich and M. Yampolsky, Dynamics of quadratic polynomials: Complex bounds for real maps,, Ann. Inst. Fourier (Grenoble), 47 (1997), 1219. doi: 10.5802/aif.1598. 
[59] 
T. Y. Li and J. Yorke, Period three implies chaos,, Amer. Math. Monthly, 82 (1975), 985. doi: 10.2307/2318254. 
[60] 
M. Martens, Distortion results and invariant Cantor sets of unimodal maps,, Erg. Th. & Dyn. Syst., 14 (1994), 331. 
[61] 
M. Martens, The periodic points of renormalization,, Ann. Math., 147 (1998), 543. doi: 10.2307/120959. 
[62] 
M. Martens and T. Nowicki, Invariant measures for Lebesgue typical quadratic maps,, Astérisque, 261 (2000), 239. 
[63] 
M. Martens and W. de Melo, The multipliers of periodic points in onedimensional dynamics,, Nonlinearity, 12 (1999), 217. doi: 10.1088/09517715/12/2/003. 
[64] 
R. M. May, Simple mathematical models with very complicated dynamics,, Nature, 261 (1976), 459. doi: 10.1038/261459a0. 
[65] 
C. McMullen, "Complex Dynamics and Renormalization,", Princeton University Press, (1994). 
[66] 
C. McMullen, "Renormalization and Three Manifolds which Fiber Over the Circle,", Princeton University Press, (1996). 
[67] 
C. McMullen, Selfsimilarity of Siegel disks and Hausdorff dimension of Julia sets,, Acta Math., 180 (1998), 247. doi: 10.1007/BF02392901. 
[68] 
M. Misiurewicz, Absolutely continuous measures for certain maps of an interval,, IHÉS Publ. Math., 53 (1981), 17. 
[69] 
M. Metropolis, M. Stein and P. Stein, On finite limit sets for transformations on the unit interval,, J. Combinatorial Theory Ser. A, 15 (1973), 25. doi: 10.1016/00973165(73)900332. 
[70] 
W. de Melo and S. van Strien, "OneDimensional Dynamics,", Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 25 (1993). 
[71] 
J. Milnor, "Dynamics in One Complex Variable,", Third edition, 160 (2006). 
[72] 
J. Milnor, On the concept of attractor,, Comm. Math. Physics, 99 (1985), 177. doi: 10.1007/BF01212280. 
[73] 
J. Milnor, Local connectivity of Julia sets: Expository lectures,, in, 274 (2000), 67. 
[74] 
J. Milnor, Fubini foiled: Katok's paradoxical example in measure theory,, Math. Intell., 19 (1997), 30. doi: 10.1007/BF03024428. 
[75] 
J. Milnor and W. Thurston, On iterated maps of the interval,, in, 1342 (1988), 1986. 
[76] 
P. J. Myrberg, Sur l'itération des polynomes réels quadratiques,, J. Math. Pures Appl. (9), 41 (1962), 339. 
[77] 
T. Nowicki and S. van Strien, Absolutely continuous measures for c^{2} unimodal maps satisfying the ColletEckmann conditions,, Invent. Math., 93 (1988), 619. doi: 10.1007/BF01410202. 
[78] 
J. Palis, A global view of dynamics and a Conjecture of the denseness of finitude of attractors,, Astérique, 261 (2000), 335. 
[79] 
E. A. Prado, Ergodicity of conformal measures for unimodal polynomials,, Conform. Geom. Dyn., 2 (1998), 29. 
[80] 
F. Przytycki and S. Rhode, Porosity of ColletEckmann Julia sets,, Fund. Math., 155 (1998), 189. 
[81] 
D. Sullivan, Quasiconformal homeomorphisms and dynamics, topology, and geometry,, in, (1986), 1216. 
[82] 
D. Sullivan, Bounds, quadratic differentials, and renormalization conjetures,, in, (1988). 
[83] 
W. Shen, Decay of geometry for unimodal maps: An elementary proof,, Annals of Math. (2), 163 (2006), 383. doi: 10.4007/annals.2006.163.383. 
[84] 
D. Smania, On the hyperbolicity of the perioddoubling fixed point,, Trans. AMS, 358 (2006), 1827. 
[85] 
M. Shishikura, The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets,, Annals of Math. (2), 147 (1998), 225. doi: 10.2307/121009. 
[86] 
M. Shishikura, Topological, geometric and complex analytic properties of Julia sets,, in, (1995), 886. 
[87] 
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