Decay of correlations in one-dimensional dynamics
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 4, pp. 621-646. 
@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] Baladi V., Viana M., Strong stochastic stability and rate of mixing for unimodal maps, Ann. Sci. Éc. Norm. Sup. 29 (1996) 483-517. | Numdam | MR | Zbl

[2] Benedicks M., Carleson L., On iterations of x↦1−ax2 on (−1,1), Ann. Math. 122 (1985) 1-25. | Zbl

[3] Benedicks M., Carleson L., The dynamics of the Hénon map, Ann. Math. 133 (1991) 73-169. | MR | Zbl

[4] Blokh A., Lyubich M., 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] Bruin H., Keller G., 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] Bruin H., Van Strien S., 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] Collet P., Statistics of closes return times for some non uniformly hyperbolic systems, Ergodic Theory Dynam. Systems 21 (2001) 401-420. | MR | Zbl

[10] Guckenheimer J., Sensitive dependence on initial conditions for unimodal maps, Comm. Math. Phys. 70 (1979) 133-160. | MR | Zbl

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

[12] Keller G., Exponents, attractors, and Hopf decompositions for interval maps, Ergodic Theory Dynam. Systems 10 (1990) 717-744. | MR | Zbl

[13] Keller G., Nowicki T., Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps, Comm. Math. Phys. 149 (1992) 31-69. | MR | Zbl

[14] Kozlovski O., Getting rid of the negative Schwarzian derivative condition, Ann. Math. 152 (2000) 743-762. | EuDML | MR | Zbl

[15] Ledrappier F., Some properties of absolutely continuous measures of an interval, Ergodic Theory Dynam. Systems 1 (1981) 77-93. | MR | Zbl

[16] Liverani C., Saussol B., Vaienti S., A probabilistic approach to intermittency, Ergodic Theory Dynam. Systems 19 (1999) 671-686. | MR | Zbl

[17] Lyubich M., Milnor J., The Fibonacci unimodal map, J. Amer. Math. Soc. 6 (1993) 425-457. | MR | Zbl

[18] Mañé R., Hyperbolicity, sinks and measure in one dimensional dynamics, Comm. Math. Phys. 100 (1985) 495-524. | MR | Zbl

[19] De Melo W., Van Strien S., One-Dimensional Dynamics, Springer, 1993. | MR | Zbl

[20] Misiurewicz M., Absolutely continuous measures for certain maps of an interval, Publ. IHÉS 53 (1981) 17-51. | EuDML | Numdam | MR | Zbl

[21] Nowicki T., Sands D., Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math. 132 (1998) 633-680. | MR | Zbl

[22] Nowicki T., Van Strien S., Absolutely continuous measures under a summability condition, Invent. Math. 105 (1991) 123-136. | EuDML | MR | Zbl

[23] Przytycki F., 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] Thunberg H., Positive Lyapunov exponents for maps with flat critical points, Ergodic Theory Dynam. Systems (1998) 767-807. | MR | Zbl

[26] Tsujii M., Small random perturbations of one-dimensional dynamical systems and Margulis-Pesin entropy formula, Random Comput. Dynam. 1 (1992) 59-89. | MR | Zbl

[27] Tsujii M., Positive Lyapunov exponents in families of one-dimensional dynamical systems, Invent. Math. 111 (1993) 113-137. | EuDML | MR | Zbl

[28] Vargas E., Measure of minimal sets of polymodal maps, Ergodic Theory Dynam. Systems 16 (1996) 159-178. | MR | Zbl

[29] Viana M., Stochastic Dynamics of Deterministic Systems, Lecture Notes, 21, Braz. Math. Colloqium, 1997.

[30] Young L.-S., Decay of correlations of certain quadratic maps, Comm. Math. Phys. 146 (1992) 123-138. | MR | Zbl

[31] Young L.-S., Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. 147 (1998) 585-650. | MR | Zbl

[32] Young L.-S., Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | MR | Zbl

Cité par Sources :