Abstract:

We will talk about the simplest non-trivial problem in Small Divisors: The Siegel problem of linearization of a holomorphic map near a fixed point. This problem and the more general problem of understanding the dynamics of a holomorhic map near a fixed point has a long history. The theory involves elements from diophantine approximation, complex function theory and Riemann surfaces, planar topology, and real dynamics. Recent progress has clarified the picture and raised new questions. We will discuss some of them.