@incollection{AST_2003__286__257_0, 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}, pages = {257--308}, publisher = {Soci\'et\'e math\'ematique de France}, number = {286}, year = {2003}, mrnumber = {2052306}, zbl = {1052.37028}, language = {en}, url = {http://www.numdam.org/item/AST_2003__286__257_0/} }
TY - CHAP AU - Colli, Eduardo AU - Pinheiro, Vilton TI - Chaos versus renormalization at quadratic $S$-unimodal Misiurewicz bifurcations BT - Geometric methods in dynamics (I) : Volume in honor of Jacob Palis AU - Collectif ED - de Melo, Wellington ED - Viana, Marcelo ED - Yoccoz, Jean-Christophe T3 - Astérisque PY - 2003 SP - 257 EP - 308 IS - 286 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2003__286__257_0/ LA - en ID - AST_2003__286__257_0 ER -
%0 Book Section %A Colli, Eduardo %A Pinheiro, Vilton %T Chaos versus renormalization at quadratic $S$-unimodal Misiurewicz bifurcations %B Geometric methods in dynamics (I) : Volume in honor of Jacob Palis %A Collectif %E de Melo, Wellington %E Viana, Marcelo %E Yoccoz, Jean-Christophe %S Astérisque %D 2003 %P 257-308 %N 286 %I Société mathématique de France %U http://www.numdam.org/item/AST_2003__286__257_0/ %G en %F AST_2003__286__257_0
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://www.numdam.org/item/AST_2003__286__257_0/
[1] Regular or stochastic dynamics in real analytic families of unimodal maps. Preprint. | MR | Zbl
, , .[2] A starting condition approach to parameter distortion in generalized renormalization. Qualitative Theory of Dynamical Systems 2 (2001), 221-288. | DOI | MR | Zbl
.[3] Generic hyperbolicity in the quadratic family. Ann. of Math. 146 (1997), 1-52. | DOI | MR | Zbl
, .[4] Absolutely continuous invariant measures for one parameter families of one dimensional maps. Comm. Math. Phys. 81 (1981), 39-88. | DOI | MR | Zbl
.[5] 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] Metric properties of non-renormalizable -unimodal maps. Part I: Induced expansion and invariant measures, Ergod. Th. & Dynam. Sys. 14 (1994), 721-755. | DOI | MR | Zbl
, .[7] Combinatorics, geometry and attractors of quasi-quadratic maps. Ann. of Math. 140 (1994), 347-404. | DOI | MR | Zbl
.[8] Dynamics of quadratic polynomials, I, II. Acta Math. 178 (1997), 185-247, 247-297. | DOI | MR | Zbl
.[9] Dynamics of quadratic polynomials, III. Parapuzzle and SBR measures. Astérisque 261 (2000), 173-200. | Numdam | MR | Zbl
.[10] Almost every real quadratic map is either regular or stochastic. Ann. of Math. 156 (2002), no. 1, 1-78. | DOI | MR | Zbl
.[11] Distortion results and invariant Cantor sets of unimodal maps. Ergod. Th. & Dynam. Sys. 14 (1994), 331-349. | DOI | MR | Zbl
.[12] Invariant measures for typical quadratic maps. Astérisque 261 (2000), 239-252. | Numdam | MR | Zbl
, .[13] One-dimensional dynamics. Springer Verlag, Berlin, Heidelberg, New York, 1993. | MR | Zbl
, .[14] Misiurewicz maps are rare. Comm. Math. Phys. 197 (1998), 109-129. | DOI | MR | Zbl
.[15] Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math 35 (1978), 260-267. | DOI | MR | Zbl
.[16] Positive Lyapunov exponent for generic one-parameter families of unimodal maps. J. Anal. Math. 64 (1994), 121-172. | DOI | MR | Zbl
, , .