# Skew products, quantitative recurrence, shrinking targets and decay of correlations

* Auteur correspondant
Abstract : We consider toral extensions of hyperbolic dynamical systems. We prove that its quantitative recurrence (also with respect to given observables) and hitting time scale behavior depend on the arithmetical properties of the extension. By this we show that those systems have a polynomial decay of correlations with respect to $C^{r}$ observables, and give estimations for its exponent, which depend on $r$ and on the arithmetical properties of the system. We also show examples of systems of this kind having not the shrinking target property, and having a trivial limit distribution of return time statistics.
Keywords :
Type de document :
Pré-publication, Document de travail
2011

http://hal.univ-brest.fr/hal-00620355
Contributeur : Benoit Saussol <>
Soumis le : mercredi 7 septembre 2011 - 16:11:14
Dernière modification le : jeudi 11 janvier 2018 - 06:16:45
Document(s) archivé(s) le : jeudi 8 décembre 2011 - 02:30:07

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skew50.pdf
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### Identifiants

• HAL Id : hal-00620355, version 1
• ARXIV : 1109.1912

### Citation

Stefano Galatolo, Jérôme Rousseau, Benoit Saussol. Skew products, quantitative recurrence, shrinking targets and decay of correlations. 2011. 〈hal-00620355〉

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