Chaos versus renormalization at quadratic S-unimodal Misiurewicz bifurcations
Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), 52 p.
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     author = {Colli, Eduardo and Pinheiro, Vilton},
     title = {Chaos versus renormalization at quadratic $S$-unimodal {Misiurewicz} bifurcations},
     booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
     editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {286},
     year = {2003},
     zbl = {1052.37028},
     mrnumber = {2052306},
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     url = {http://www.numdam.org/item/AST_2003__286__257_0/}
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Colli, Eduardo; Pinheiro, Vilton. Chaos versus renormalization at quadratic $S$-unimodal Misiurewicz bifurcations, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), 52 p. http://www.numdam.org/item/AST_2003__286__257_0/

[1] A. Ávila, M. Lyubich, W. De Melo. Regular or stochastic dynamics in real analytic families of unimodal maps. Preprint. | MR 2018784 | Zbl 1050.37018

[2] E. Colli. A starting condition approach to parameter distortion in generalized renormalization. Qualitative Theory of Dynamical Systems 2 (2001), 221-288. | Article | MR 1913287 | Zbl 1064.37028

[3] J. Graczyk, G. Świątek. Generic hyperbolicity in the quadratic family. Ann. of Math. 146 (1997), 1-52. | Article | MR 1469316 | Zbl 0936.37015

[4] M. Jakobson. Absolutely continuous invariant measures for one parameter families of one dimensional maps. Comm. Math. Phys. 81 (1981), 39-88. | Article | MR 630331 | Zbl 0497.58017

[5] M. Jakobson. Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions. Proceedings of Symposia in Pure Mathematics 69 (2001), 825-881. | Article | MR 1858558 | Zbl 1006.37016

[6] M. Jakobson, G. Świątek. Metric properties of non-renormalizable S-unimodal maps. Part I: Induced expansion and invariant measures, Ergod. Th. & Dynam. Sys. 14 (1994), 721-755. | Article | MR 1304140 | Zbl 0830.58019

[7] M. Lyubich. Combinatorics, geometry and attractors of quasi-quadratic maps. Ann. of Math. 140 (1994), 347-404. | Article | MR 1298717 | Zbl 0821.58014

[8] M. Lyubich. Dynamics of quadratic polynomials, I, II. Acta Math. 178 (1997), 185-247, 247-297. | Article | MR 1459261 | Zbl 0908.58053

[9] M. Lyubich. Dynamics of quadratic polynomials, III. Parapuzzle and SBR measures. Astérisque 261 (2000), 173-200. | Numdam | MR 1755441 | Zbl 1044.37038

[10] M. Lyubich. Almost every real quadratic map is either regular or stochastic. Ann. of Math. 156 (2002), no. 1, 1-78. | Article | MR 1935840 | Zbl 1160.37356

[11] M. Martens. Distortion results and invariant Cantor sets of unimodal maps. Ergod. Th. & Dynam. Sys. 14 (1994), 331-349. | Article | MR 1279474 | Zbl 0809.58026

[12] M. Martens, T. Nowicki. Invariant measures for typical quadratic maps. Astérisque 261 (2000), 239-252. | Numdam | MR 1755443 | Zbl 0939.37020

[13] W. De Melo, S. Van Strien. One-dimensional dynamics. Springer Verlag, Berlin, Heidelberg, New York, 1993. | MR 1239171 | Zbl 0791.58003

[14] D. Sands. Misiurewicz maps are rare. Comm. Math. Phys. 197 (1998), 109-129. | Article | MR 1646471 | Zbl 0921.58015

[15] D. Singer. Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math 35 (1978), 260-267. | Article | MR 494306 | Zbl 0391.58014

[16] Ph. Thieullen, C. Tresser, L. S. Young. Positive Lyapunov exponent for generic one-parameter families of unimodal maps. J. Anal. Math. 64 (1994), 121-172. | Article | MR 1303510 | Zbl 0821.58015