Decay of correlations for nonuniformly expanding systems

Sébastien Gouëzel

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 1, page 1-31
  • ISSN: 0037-9484

Abstract

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We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in O ( e - c n ) .

How to cite

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Gouëzel, Sébastien. "Decay of correlations for nonuniformly expanding systems." Bulletin de la Société Mathématique de France 134.1 (2006): 1-31. <http://eudml.org/doc/272509>.

@article{Gouëzel2006,
abstract = {We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in $O(\rm e ^\{-c \sqrt\{n\}\})$.},
author = {Gouëzel, Sébastien},
journal = {Bulletin de la Société Mathématique de France},
keywords = {decay of correlations; Young tower; non uniformly expanding maps},
language = {eng},
number = {1},
pages = {1-31},
publisher = {Société mathématique de France},
title = {Decay of correlations for nonuniformly expanding systems},
url = {http://eudml.org/doc/272509},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Gouëzel, Sébastien
TI - Decay of correlations for nonuniformly expanding systems
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 1
SP - 1
EP - 31
AB - We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in $O(\rm e ^{-c \sqrt{n}})$.
LA - eng
KW - decay of correlations; Young tower; non uniformly expanding maps
UR - http://eudml.org/doc/272509
ER -

References

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  3. [3] J. F. Alves & V. Araújo – « Random perturbations of nonuniformly expanding maps », Astérisque286 (2003), p. 25–62. Zbl1043.37016MR2052296
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  8. [8] V. Baladi & S. Gouëzel – « Stretched exponential bounds for the correlations of the Viana-Alves skew product », www.math.jussieu.fr/~baladi, to appear, Proceedings Workshop on Dynamics and Randomness, Universidad de Chile, Santiago de Chile, 2002. MR1858537
  9. [9] —, « A note on stretched exponential decay of correlations for the Viana-Alves map », arXiv.org/math.DS/0311189, 2003. 
  10. [10] J. Buzzi, O. Sester & M. Tsujii – « Weakly expanding skew-products of quadratic maps », Ergodic Theory Dynam. Systems23 (2003), p. 1401–1414. Zbl1037.37014MR2018605
  11. [11] S. Gouëzel – « Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes », Thèse, Université Paris Sud, 2004. 
  12. [12] M. Viana – « Multidimensional nonhyperbolic attractors », Publ. Math. IHÉS85 (1997), p. 63–96. Zbl1037.37016MR1471866
  13. [13] L.-S. Young – « Statistical properties of dynamical systems with some hyperbolicity », Ann. of Math.147 (1998), p. 585–650. Zbl0945.37009MR1637655
  14. [14] —, « Recurrence times and rates of mixing », Israel J. Math.110 (1999), p. 153–188. Zbl0983.37005MR1750438

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