Sinai-Bowen-Ruelle measures for certain Hénon maps

@article{Benedicks1993SinaiBowenRuelleMF,
  title={Sinai-Bowen-Ruelle measures for certain H{\'e}non maps},
  author={Michael Benedicks and Lai-Sang Young},
  journal={Inventiones mathematicae},
  year={1993},
  volume={112},
  pages={541-576}
}
0. Introduction. We study maps T a;b : R 2 ! R 2 deened by T a;b (x; y) = (1 ax 2 + y; bx); 0 < a < 2; b > 0: In BC2] it was proved that for a positive measure set of parameters (a; b), T a;b has a topologically transitive attractor = a;b on which there is some hyperbolic behavior. The aim of this paper is to study the statistical properties of these attractors. Using the machinery developed in BC2] we prove the following Theorem. There is a set R 2 with Leb(() > 0 such that for all (a; b) 2… 
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