Decay of correlations in one-dimensional dynamics
Henk Bruin; Stefano Luzzatto; Sebastian Van Strien
Annales scientifiques de l'École Normale Supérieure (2003)
- Volume: 36, Issue: 4, page 621-646
- ISSN: 0012-9593
Access Full Article
topHow to cite
topBruin, Henk, Luzzatto, Stefano, and Van Strien, Sebastian. "Decay of correlations in one-dimensional dynamics." Annales scientifiques de l'École Normale Supérieure 36.4 (2003): 621-646. <http://eudml.org/doc/82613>.
@article{Bruin2003,
author = {Bruin, Henk, Luzzatto, Stefano, Van Strien, Sebastian},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {interval maps; summability condition; central limit theorem; decay of correlations},
language = {eng},
number = {4},
pages = {621-646},
publisher = {Elsevier},
title = {Decay of correlations in one-dimensional dynamics},
url = {http://eudml.org/doc/82613},
volume = {36},
year = {2003},
}
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
PB - Elsevier
VL - 36
IS - 4
SP - 621
EP - 646
LA - eng
KW - interval maps; summability condition; central limit theorem; decay of correlations
UR - http://eudml.org/doc/82613
ER -
References
top- [1] Baladi V., Viana M., Strong stochastic stability and rate of mixing for unimodal maps, Ann. Sci. Éc. Norm. Sup.29 (1996) 483-517. Zbl0868.58051MR1386223
- [2] Benedicks M., Carleson L., On iterations of x↦1−ax2 on (−1,1), Ann. Math.122 (1985) 1-25. Zbl0597.58016
- [3] Benedicks M., Carleson L., The dynamics of the Hénon map, Ann. Math.133 (1991) 73-169. Zbl0724.58042MR1087346
- [4] Blokh A., Lyubich M., Measurable dynamics of S-unimodal maps, Ann. Sci. Éc. Norm. Sup.24 (1991) 545-573. Zbl0790.58024MR1132757
- [5] Bruin H., Luzzatto S., van Strien S., Decay of correlation in one-dimensional dynamics, Preprint IHÉS, 1999. Zbl1039.37021MR1858488
- [6] Bruin H., Keller G., Equilibrium states for S-unimodal maps, Ergodic Theory Dynam. Systems18 (1998) 765-789. Zbl0916.58020MR1645373
- [7] Bruin H., van Strien S., Expansion of derivatives in one-dimensional dynamics, Israel J. Math. (to appear). Zbl1122.37310MR2013358
- [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. Zbl1198.37066
- [9] Collet P., Statistics of closes return times for some non uniformly hyperbolic systems, Ergodic Theory Dynam. Systems21 (2001) 401-420. Zbl1002.37019MR1827111
- [10] Guckenheimer J., Sensitive dependence on initial conditions for unimodal maps, Comm. Math. Phys.70 (1979) 133-160. Zbl0429.58012MR553966
- [11] Jakobson M.V., Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys.81 (1981) 39-88. Zbl0497.58017MR630331
- [12] Keller G., Exponents, attractors, and Hopf decompositions for interval maps, Ergodic Theory Dynam. Systems10 (1990) 717-744. Zbl0715.58020MR1091423
- [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. Zbl0763.58024MR1182410
- [14] Kozlovski O., Getting rid of the negative Schwarzian derivative condition, Ann. Math.152 (2000) 743-762. Zbl0988.37044MR1815700
- [15] Ledrappier F., Some properties of absolutely continuous measures of an interval, Ergodic Theory Dynam. Systems1 (1981) 77-93. Zbl0487.28015MR627788
- [16] Liverani C., Saussol B., Vaienti S., A probabilistic approach to intermittency, Ergodic Theory Dynam. Systems19 (1999) 671-686. Zbl0988.37035MR1695915
- [17] Lyubich M., Milnor J., The Fibonacci unimodal map, J. Amer. Math. Soc.6 (1993) 425-457. Zbl0778.58040MR1182670
- [18] Mañé R., Hyperbolicity, sinks and measure in one dimensional dynamics, Comm. Math. Phys.100 (1985) 495-524. Zbl0583.58016MR806250
- [19] de Melo W., van Strien S., One-Dimensional Dynamics, Springer, 1993. Zbl0791.58003MR1239171
- [20] Misiurewicz M., Absolutely continuous measures for certain maps of an interval, Publ. IHÉS53 (1981) 17-51. Zbl0477.58020MR623533
- [21] Nowicki T., Sands D., Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math.132 (1998) 633-680. Zbl0908.58016MR1625708
- [22] Nowicki T., van Strien S., Absolutely continuous measures under a summability condition, Invent. Math.105 (1991) 123-136. Zbl0736.58030MR1109621
- [23] Przytycki F., Iterations of holomorphic Collet–Eckmann maps: conformal and invariant measures, Trans. Amer. Math. Soc.350 (1998) 717-742. Zbl0892.58063MR1407501
- [24] van Strien S., Vargas E., Real bounds, ergodicity and negative Schwarzian for multimodal maps, Preprint, 2000 and 2001. Zbl1073.37043
- [25] Thunberg H., Positive Lyapunov exponents for maps with flat critical points, Ergodic Theory Dynam. Systems (1998) 767-807. Zbl0966.37011MR1695920
- [26] Tsujii M., Small random perturbations of one-dimensional dynamical systems and Margulis–Pesin entropy formula, Random Comput. Dynam.1 (1992) 59-89. Zbl0783.58018MR1181380
- [27] Tsujii M., Positive Lyapunov exponents in families of one-dimensional dynamical systems, Invent. Math.111 (1993) 113-137. Zbl0787.58029MR1193600
- [28] Vargas E., Measure of minimal sets of polymodal maps, Ergodic Theory Dynam. Systems16 (1996) 159-178. Zbl0851.58015MR1375131
- [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. Zbl0760.58030MR1163671
- [31] Young L.-S., Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math.147 (1998) 585-650. Zbl0945.37009MR1637655
- [32] Young L.-S., Recurrence times and rates of mixing, Israel J. Math.110 (1999) 153-188. Zbl0983.37005MR1750438
Citations in EuDML Documents
top- Sébastien Gouëzel, Berry–Esseen theorem and local limit theorem for non uniformly expanding maps
- Feliks Przytycki, Juan Rivera-Letelier, Statistical properties of topological Collet–Eckmann maps
- José F. Alves, Stefano Luzzatto, Vilton Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems
- Henk Bruin, Mike Todd, Equilibrium states for interval maps: the potential
- Henk Bruin, Weixiao Shen, Sebastian Van Strien, Existence of unique SRB-measures is typical for real unicritical polynomial families
- Viviane Baladi, Daniel Smania, Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.