Random versus deterministic exponents in a rich family of   diffeomorphisms
  We study, both numerically and theoretically, the relationship between the random Lyapunov exponent of a family of area preserving diffeomorphisms of the 2-sphere and the mean of the Lyapunov exponents of the individual members. 
Francois Ledrappier, Michael Shub, Carles Simo, Amie Wilkinson