For every C-2-small function B, we prove that the map (x, y) bar right arrow (x(2 )+ a, 0) B (x , y, a) leaves invariant a physical, SRB probability measure, for a set of parameters a of positive Lebesgue measure. When the perturbation B is zero, this is the Jakobson Theorem; when the perturbation is a small constant times (0, x), this is the celebrated Benedicks-Carleson theorem.
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