Geodesic
Statistical properties of unimodal maps: the quadratic family
Artur Ávila1 ; Carlos Gustavo Moreira2
1 CNRS UMR 7599, Université Pierre et Marie Curie, 75005 Paris, France
2 IMPA, Rio de Janeiro, 22460-320, Brazil
Annals of mathematics, Tome 161 (2005) no. 2, pp. 831-881

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We prove that almost every nonregular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step in achieving the same results for more general families of unimodal maps.

DOI : 10.4007/annals.2005.161.831

Artur Ávila 1 ; Carlos Gustavo Moreira 2

1 CNRS UMR 7599, Université Pierre et Marie Curie, 75005 Paris, France
2 IMPA, Rio de Janeiro, 22460-320, Brazil 
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Artur Ávila; Carlos Gustavo Moreira. Statistical properties of unimodal maps: the quadratic family. Annals of mathematics, Tome 161 (2005) no. 2, pp. 831-881. doi: 10.4007/annals.2005.161.831

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