Monotone families of circle diffeomorphisms driven by expandingcircle maps

Abstract: We consider monotone families of circle diffeomorphisms forced
by strongly expanding circle maps. We obtain estimates of the fibered
Lyapunov exponents for such systems and show that in the limit as the
expansion tends to infinity, they approach the values of the Lyapunov
exponents for the corresponding random case. The estimates are based on a
control of the distribution of the iterates of almost every point, up to a
fixed (small) scale, depending on the expansion.
This is joint work with Raphaël Krikorian.