Exponential decay of hyperbolic times for Benedicks-Carleson quadratic maps (Q616631)

In [Ann. Math. (2) 122, 1--25 (1985; Zbl 0597.58016)] \textit{M. Benedicks} and \textit{L. Carleson} (BC) studied maps of the form \(f_ax)= 1- ax^2\) of \((-1,1)\), and introduced a special set of parameters BC satisfying two conditions on the iterates. The present author proves that the tail of the hyperbolic times introduced by J. F. Alves et al. decays exponentially fast. This improves previus work of the same author, where subexponential rates have been obtained. The sharper estimates allow to use the theory developed by Alves et al. to recover statistical properties of these maps.