Chaos versus renormalization at quadratic S-unimodal Misiurewicz bifurcations
Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 257-308. 
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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},
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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), pp. 257-308. http://archive.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 | Zbl

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

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

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

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

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

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

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

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

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

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

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

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

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

[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. | DOI | MR | Zbl