Georgia Institute of Technology College of Sciences

Given f: \C \times T^1 to itself, an analytic perturbation of a fibered rotation map , we will present two proofs of existence of an analytic conjugation of f to the fibered rotation , on a neighborhood of {0} \times T^1. This talk will be self- contained except for some usual "tricks" from KAM theory and which will be explained better in another talk. In the talk we will discuss carefully the number theoretic conditions on the fibered rotation needed to obtain the theorem.