@incollection{AST_2003__286__81_0, author = {Avila, Artur and Moreira, Carlos Gustavo}, title = {Statistical properties of unimodal maps: smooth families with negative {Schwarzian} derivative}, 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 = {81--118}, publisher = {Soci\'et\'e math\'ematique de France}, number = {286}, year = {2003}, mrnumber = {2052298}, zbl = {1046.37021}, language = {en}, url = {http://archive.numdam.org/item/AST_2003__286__81_0/} }
TY - CHAP AU - Avila, Artur AU - Moreira, Carlos Gustavo TI - Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative 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 - 81 EP - 118 IS - 286 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2003__286__81_0/ LA - en ID - AST_2003__286__81_0 ER -
%0 Book Section %A Avila, Artur %A Moreira, Carlos Gustavo %T Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative %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 81-118 %N 286 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2003__286__81_0/ %G en %F AST_2003__286__81_0
Avila, Artur; Moreira, Carlos Gustavo. Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative, in Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 81-118. http://archive.numdam.org/item/AST_2003__286__81_0/
[Ar] Dynamical systems. In "Development of mathematics 1950-2000", 33-61, Birkhäuser, Basel, 2000. | DOI | MR | Zbl
.[A] Bifurcations of unimodal maps: the topologic and metric picture. IMPA Thesis (2001) www.math.sunysb.edu/~artur/. | Zbl
.[ALM] Regular or stochastic dynamics in real analytic families of unimodal maps. Preprint IMS at Stony Brook, #2001/15. To appear in Invent. Math. | MR | Zbl
, and .[AM1] Statistical properties of unimodal maps: the quadratic family. Preprint www.arXiv.org. To appear in Annals of Math. | MR | Zbl
, .[AM2] Statistical properties of unimodal maps: physical measures, periodic orbits and pathological laminations. Preprint www.arXiv.org. | DOI | MR | Zbl
, .[AM3] Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family. Preprint www.arXiv.org. | DOI | MR | Zbl
, .[AM4] Phase-Parameter relation and sharp statistical properties in general families of unimodal maps. Preprint www.arXiv.org. | DOI | MR | Zbl
, .[BBM] Almost sure rates of mixing for i.i.d. unimodal maps. Ann. Sci. Ecole Norm. Sup. (4), v. 35 (2002), no. 1, 77-126. | DOI | EuDML | Numdam | MR | Zbl
, and .[BV] Strong stochastic stability and rate of mixing for unimodal maps. Ann. Sci. Ecole Norm. Sup. (4), v. 29 (1996), no. 4, 483-517. | DOI | EuDML | Numdam | MR | Zbl
and .[BC] On iterations of on . Ann. Math., v. 122 (1985), 1-25. | MR | Zbl
and .[GS] Generic hyperbolicity in the logistic family. Ann. of Math., v. 146 (1997), 1-52. | DOI | MR | Zbl
and .[J] Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. Comm. Math. Phys., v. 81 (1981), 39-88. | DOI | MR | Zbl
.[KN] Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps. Comm. Math. Phys., 149 (1992), 31-69. | DOI | MR | Zbl
and .[K] Structural stability in one-dimensional dynamics. Thesis (1998).
.[L1] Combinatorics, geometry and attractors of quasi-quadratic maps. Ann. Math, 140 (1994), 347-404. | DOI | MR | Zbl
.[L2] Dynamics of quadratic polynomials, I-II. Acta Math., 178 (1997), 185-297. | DOI | MR | Zbl
.[L3] Dynamics of quadratic polynomials, III. Parapuzzle and SBR measure. Preprint IMS at Stony Brook, # 1995/5. Astérisque, v. 261 (2000), 173-200. | Numdam | MR | Zbl
.[L4] Almost every real quadratic map is either regular or stochastic. Ann. of Math. (2) 156 (2002), no. 1, 1-78. | DOI | MR | Zbl
.[MN] Invariant measures for Lebesgue typical quadratic maps. Preprint IMS at Stony Brook, # 1996/6. Astérisque, v. 261 (2000), 239-252. | Numdam | MR | Zbl
and .[MvS] One-dimensional dynamics. Springer, 1993. | MR | Zbl
and .[NP1] The conjugacy of Collet-Eckmann's map of the interval with the tent map is Hölder continuous. Ergodic Theory Dynam. Systems 9 (1989), no. 2, 379-388. | DOI | MR | Zbl
and .[NP2] Topological invariance of the Collet-Eckmann property for S-unimodal maps. Fund. Math. 155 (1998), no. 1, 33-43. | EuDML | MR | Zbl
and .[NS] Non-uniform hyperbolicity and universal bounds for S-unimodal maps. Invent. Math. 132 (1998), no. 3, 633-680. | DOI | MR | Zbl
and .[Pa] A global view of dynamics and a conjecture of the denseness of finitude of attractors. Astérisque, v. 261 (2000), 335-347. | Numdam | MR | Zbl
.[T1] Positive Lyapunov exponents in families of one dimensional dynamical systems. Invent. Math. 111 (1993), 113-137. | DOI | EuDML | MR | Zbl
.[T2] Small random perturbations of one dimensional dynamical systems and Margulis-Pesin entropy formula. Random & Comput. Dynamics. Vol.1 No.1 59-89, (1992). | MR | Zbl
.[Y] Decay of correlations for certain quadratic maps. Comm. Math. Phys., 146 (1992), 123-138. | DOI | MR | Zbl
.