Exponential decay of hyperbolic times for Benedicks–Carleson quadratic maps

Freitas, Jorge Milhazes

doi:10.4171/PM/1876

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Portugaliae Mathematica

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Volume 67, Issue 4, 2010, pp. 525–540

DOI: 10.4171/PM/1876

Published online: 2010-11-24

Exponential decay of hyperbolic times for Benedicks–Carleson quadratic maps

Jorge Milhazes Freitas^[1]

(1) Universidade do Porto, Portugal

We consider the Benedicks–Carleson quadratic maps and prove that the tail of Hyperbolic Times, introduced in [5], decays exponentially fast. This improves a previous work [14], where subexponential estimates for this tail were obtained and allows to use the theory developed by Alves et al as another approach to recover statistical properties of these maps like exponential Decay of Correlations, Large Deviations, Central Limit Theorem, Statistical Stability and continuity of metric entropy.

Keywords: Logistic family, hyperbolic times, statistical properties, tail sets

Freitas Jorge Milhazes: Exponential decay of hyperbolic times for Benedicks–Carleson quadratic maps. Port. Math. 67 (2010), 525-540. doi: 10.4171/PM/1876