Second Phase transition line
  We study the phase transion line of the almost Mathieu operator, that separates arithmetic regions corresponding to singular continuous and a.e. pure point regimes, and prove that both purely singular continuous and a.e. pure point spectrum occur for dense sets of frequencies. 
Artur Avila, Svetlana Jitomirskaya, Qi Zhou
math-ph math.DS math.MP math.SP