@article{ASENS_2003_4_36_4_621_0, author = {Bruin, Henk and Luzzatto, Stefano and Van Strien, Sebastian}, title = {Decay of correlations in one-dimensional dynamics}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {621--646}, publisher = {Elsevier}, volume = {Ser. 4, 36}, number = {4}, year = {2003}, doi = {10.1016/S0012-9593(03)00025-9}, mrnumber = {2013929}, zbl = {1039.37021}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S0012-9593(03)00025-9/} }
TY - JOUR AU - Bruin, Henk AU - Luzzatto, Stefano AU - Van Strien, Sebastian TI - Decay of correlations in one-dimensional dynamics JO - Annales scientifiques de l'École Normale Supérieure PY - 2003 SP - 621 EP - 646 VL - 36 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S0012-9593(03)00025-9/ DO - 10.1016/S0012-9593(03)00025-9 LA - en ID - ASENS_2003_4_36_4_621_0 ER -
%0 Journal Article %A Bruin, Henk %A Luzzatto, Stefano %A Van Strien, Sebastian %T Decay of correlations in one-dimensional dynamics %J Annales scientifiques de l'École Normale Supérieure %D 2003 %P 621-646 %V 36 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/S0012-9593(03)00025-9/ %R 10.1016/S0012-9593(03)00025-9 %G en %F ASENS_2003_4_36_4_621_0
Bruin, Henk; Luzzatto, Stefano; Van Strien, Sebastian. Decay of correlations in one-dimensional dynamics. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 4, pp. 621-646. doi : 10.1016/S0012-9593(03)00025-9. http://www.numdam.org/articles/10.1016/S0012-9593(03)00025-9/
[1] Strong stochastic stability and rate of mixing for unimodal maps, Ann. Sci. Éc. Norm. Sup. 29 (1996) 483-517. | Numdam | MR | Zbl
, ,[2] On iterations of x↦1−ax2 on (−1,1), Ann. Math. 122 (1985) 1-25. | Zbl
, ,[3] The dynamics of the Hénon map, Ann. Math. 133 (1991) 73-169. | MR | Zbl
, ,[4] Measurable dynamics of S-unimodal maps, Ann. Sci. Éc. Norm. Sup. 24 (1991) 545-573. | Numdam | MR | Zbl
, ,[5] Bruin H., Luzzatto S., van Strien S., Decay of correlation in one-dimensional dynamics, Preprint IHÉS, 1999.
[6] Equilibrium states for S-unimodal maps, Ergodic Theory Dynam. Systems 18 (1998) 765-789. | MR | Zbl
, ,[7] Bruin H., van Strien S., Expansion of derivatives in one-dimensional dynamics, Israel J. Math. (to appear). | MR | Zbl
[8] Existence of acips for multimodal maps, in: Global Analysis of Dynamical Systems, Festschrift to Floris Takens for his 60th birthday, IOP Publishing, Bristol, 2001, pp. 433-447. | Zbl
, ,[9] Statistics of closes return times for some non uniformly hyperbolic systems, Ergodic Theory Dynam. Systems 21 (2001) 401-420. | MR | Zbl
,[10] Sensitive dependence on initial conditions for unimodal maps, Comm. Math. Phys. 70 (1979) 133-160. | MR | Zbl
,[11] Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981) 39-88. | MR | Zbl
,[12] Exponents, attractors, and Hopf decompositions for interval maps, Ergodic Theory Dynam. Systems 10 (1990) 717-744. | MR | Zbl
,[13] Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps, Comm. Math. Phys. 149 (1992) 31-69. | MR | Zbl
, ,[14] Getting rid of the negative Schwarzian derivative condition, Ann. Math. 152 (2000) 743-762. | EuDML | MR | Zbl
,[15] Some properties of absolutely continuous measures of an interval, Ergodic Theory Dynam. Systems 1 (1981) 77-93. | MR | Zbl
,[16] A probabilistic approach to intermittency, Ergodic Theory Dynam. Systems 19 (1999) 671-686. | MR | Zbl
, , ,[17] The Fibonacci unimodal map, J. Amer. Math. Soc. 6 (1993) 425-457. | MR | Zbl
, ,[18] Hyperbolicity, sinks and measure in one dimensional dynamics, Comm. Math. Phys. 100 (1985) 495-524. | MR | Zbl
,[19] One-Dimensional Dynamics, Springer, 1993. | MR | Zbl
, ,[20] Absolutely continuous measures for certain maps of an interval, Publ. IHÉS 53 (1981) 17-51. | EuDML | Numdam | MR | Zbl
,[21] Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math. 132 (1998) 633-680. | MR | Zbl
, ,[22] Absolutely continuous measures under a summability condition, Invent. Math. 105 (1991) 123-136. | EuDML | MR | Zbl
, ,[23] Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures, Trans. Amer. Math. Soc. 350 (1998) 717-742. | MR | Zbl
,[24] van Strien S., Vargas E., Real bounds, ergodicity and negative Schwarzian for multimodal maps, Preprint, 2000 and 2001. | Zbl
[25] Positive Lyapunov exponents for maps with flat critical points, Ergodic Theory Dynam. Systems (1998) 767-807. | MR | Zbl
,[26] Small random perturbations of one-dimensional dynamical systems and Margulis-Pesin entropy formula, Random Comput. Dynam. 1 (1992) 59-89. | MR | Zbl
,[27] Positive Lyapunov exponents in families of one-dimensional dynamical systems, Invent. Math. 111 (1993) 113-137. | EuDML | MR | Zbl
,[28] Measure of minimal sets of polymodal maps, Ergodic Theory Dynam. Systems 16 (1996) 159-178. | MR | Zbl
,[29] Stochastic Dynamics of Deterministic Systems, Lecture Notes, 21, Braz. Math. Colloqium, 1997.
,[30] Decay of correlations of certain quadratic maps, Comm. Math. Phys. 146 (1992) 123-138. | MR | Zbl
,[31] Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. 147 (1998) 585-650. | MR | Zbl
,[32] Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | MR | Zbl
,Cité par Sources :