Georgia Institute of Technology College of Sciences

We first discuss the construction of whiskered invariant tori for fibered holomorphic dynamics using a Nash-Moser iteration. The results are in a-posteriori form. The iterative procedure we present has numerical applications (it lends itself to efficient numerical implementations) since it is not based on transformation theory but rather in applying corrections which ameliorate notably the curse of dimensionality. Then we will discuss results on compensated domains in a Banach space.