Skew products, quantitative recurrence, shrinking targets and decay of correlations
Dynamical Systems
2015-08-05 v1
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 observables, and give estimations for its exponent, which depend on 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
Cite
@article{arxiv.1109.1912,
title = {Skew products, quantitative recurrence, shrinking targets and decay of correlations},
author = {Stefano Galatolo and Jérôme Rousseau and Benoît Saussol},
journal= {arXiv preprint arXiv:1109.1912},
year = {2015}
}