Construction of whiskered invariant tori for fibered holomorphic dynamics (I: Reducibility).

Series: 
Dynamical Systems Working Seminar
Tuesday, October 6, 2015 - 17:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
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. The asymptotic properties of the derivative cocycle A_K  play a crucial role: In this first talk we will find suitable geometric and number-theoretic conditions for A_K. Later, we will see how to relax these conditions.