Weakly expanding skew-products of quadratic maps

@article{Buzzi2003WeaklyES,
  title={Weakly expanding skew-products of quadratic maps},
  author={J{\'e}r{\^o}me Buzzi and Olivier Sester and Masato Tsujii},
  journal={Ergodic Theory and Dynamical Systems},
  year={2003},
  volume={23},
  pages={1401 - 1414}
}
We consider quadratic skew-products over angle-doubling of the circle and prove that they admit positive Lyapunov exponents almost everywhere and an absolutely continuous invariant probability measure. This extends corresponding results of M. Viana and J. F. Alvès for skew-products over the linear strongly expanding map of the circle. 
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