Georgia Institute of Technology College of Sciences

We consider fibered holomorphic dynamics, generated by a skew product over an irrational translation of the torus. The invariant object that organizes the dynamics is an invariant torus. Often one can find an approximately invariant torus K_0, and we construct an invariant torus, starting from K_0. The main technique is a KAM iteration in a-posteriori format. In this talk we give the details of the iterative procedure using the geometric and number-theoretic conditions presented last time.