Full measure reducibility and localization for Jacobi operators: a   topological criterion
  We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase transition for the extended Harper's model in the positive Lyapunov exponent region. 
Rui Han and Svetlana Jitomirskaya
math.SP math-ph math.MP