Analytic skew-products of quadratic polynomials over   Misiurewicz-Thurston maps
  We consider skew-products of quadratic maps over certain Misiurewicz-Thurston maps and study their statistical properties. We prove that, when the coupling function is a polynomial of odd degree, such a system admits two positive Lyapunov exponents almost everywhere and a unique absolutely continuous invariant probability measure. 
Rui Gao, Weixiao Shen
math.DS