Strong stochastic stability and rate of mixing for unimodal maps

Viviane Baladi; Marcelo Viana

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 4, page 483-517
  • ISSN: 0012-9593

How to cite

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Baladi, Viviane, and Viana, Marcelo. "Strong stochastic stability and rate of mixing for unimodal maps." Annales scientifiques de l'École Normale Supérieure 29.4 (1996): 483-517. <http://eudml.org/doc/82414>.

@article{Baladi1996,
author = {Baladi, Viviane, Viana, Marcelo},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {unimodal map; stable under random perturbations},
language = {eng},
number = {4},
pages = {483-517},
publisher = {Elsevier},
title = {Strong stochastic stability and rate of mixing for unimodal maps},
url = {http://eudml.org/doc/82414},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Baladi, Viviane
AU - Viana, Marcelo
TI - Strong stochastic stability and rate of mixing for unimodal maps
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 4
SP - 483
EP - 517
LA - eng
KW - unimodal map; stable under random perturbations
UR - http://eudml.org/doc/82414
ER -

References

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  1. [BaY] V. BALADI and L.-S. YOUNG, On the spectra of randomly perturbed expanding maps (see also Erratum, Comm. Math. Phys., Vol. 166, 1984, pp. 219-220, Comm. Math. Phys., Vol. 156, 1993, pp. 355-385). Zbl0814.60102MR94g:58172
  2. [BC] M. BENEDICKS and L. CARLESON, The dynamics of the Hénon map (Ann. of Math., 2, Vol. 133, 1991, pp. 73-169). Zbl0724.58042MR92d:58116
  3. [BY1] M. BENEDICKS and L.-S. YOUNG, Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps (Ergodic Theory Dynamical Systems, Vol. 12, 1992, pp. 13-37). Zbl0769.58051MR93d:58087
  4. [BY2] M. BENEDICKS and L.-S. YOUNG, SBR-measures for certain Hénon maps (Invent. Math., Vol. 112, 1993, pp. 541-576). Zbl0796.58025MR94e:58074
  5. [BL] A. M. BLOKH and M. Yu. LYUBICH, Measurable dynamics of S-unimodal maps of the interval (Ann. Scient. École Norm. Sup., Vol. 24, 1991, pp. 545-573). Zbl0790.58024MR93f:58132
  6. [Co] P. COLLET, Ergodic properties of some unimodal mappings of the interval (Preprint 11 Institute Mittag Leffler (unpublished), 1984). 
  7. [Ja] M. JAKOBSON, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps (Comm. Math. Phys., Vol. 81, 1981, pp. 39-88). Zbl0497.58017MR83j:58070
  8. [KK] A. KATOK and Y. KIFER, Random perturbations of transformations of an interval (J. Analyse Math., Vol. 47, 1986, pp. 193-237). Zbl0616.60064MR88c:58053
  9. [KN] G. KELLER and T. NOWICKI, Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps (Comm. Math. Phys., Vol. 149, 1992, pp. 31-69). Zbl0763.58024MR93i:58123
  10. [Ki1] Y. KIFER, Ergodic Theory of Random Perturbations (Birkhäuser, Boston Basel, 1986). 
  11. [Ki2] Y. KIFER, Random Perturbations of Dynamical Systems (Birkhäuser, Boston, Basel, 1988). Zbl0659.58003MR91e:58159
  12. [LY] A. LASOTA and J. A. YORKE, On the existence of invariant measures for piecewise monotonic transformations (Trans. Amer. Math. Soc., Vol. 186, 1973, pp. 481-488). Zbl0298.28015MR49 #538
  13. [Le] F. LEDRAPPIER, Some properties of absolutely continuous invariant measures on an interval (Ergodic Theory Dynamical Systems 1, 1981, pp. 77-93). Zbl0487.28015MR82k:28018
  14. [MS] W. de MELO and S. van STRIEN, One-dimensional Dynamics (Springer-Verlag, Berlin, 1993). Zbl0791.58003MR95a:58035
  15. [No] T. NOWICKI, A positive Lyapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity (Ergodic Theory Dynamical Systems 8, 1988, pp. 425-435). Zbl0638.58021MR90c:58100
  16. [Ry] M. RYCHLIK, Bounded variation and invariant measures (Studia Math., LXXVI, 1983, pp. 69-80). Zbl0575.28011MR85h:28019
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  18. [Yo] L.-S. YOUNG, Decay of correlations for certain quadratic maps (Comm. Math. Phys., Vol. 146, 1992, pp. 123-138). Zbl0760.58030MR93j:58083

Citations in EuDML Documents

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  1. Anastasia Maltseva, Volker Reitmann, Bifurcations of invariant measures in discrete-time parameter dependent cocycles
  2. Roger J. Metzger, Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows
  3. Viviane Baladi, Michael Benedicks, Véronique Maume-Deschamps, Almost sure rates of mixing for i.i.d. unimodal maps
  4. Michael Benedicks, Marcelo Viana, Random perturbations and statistical properties of Hénon-like maps
  5. Henk Bruin, Stefano Luzzatto, Sebastian Van Strien, Decay of correlations in one-dimensional dynamics
  6. Viviane Baladi, Daniel Smania, Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps

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