J. Bourgain, S. Jitomirskaya
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
(198K, postscript)

ABSTRACT.  We study regularity properties of the Lyapunov exponent L of quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. 
We prove joint continuity of L, in frequency and energy, at every irrational frequency.