Exponential decay of hyperbolic times for Benedicks–Carleson quadratic maps

Abstract

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.