Nataliya Goncharuk (Cornell University)

Title:
Complex rotation numbers and bubbles

Abstract:
Given a complex number w, Im w>0, and an analytic circle
diffeomorphism f:R/Z->R/Z, one can construct a complex torus by glueing an annulus  A_w = (0< Im z < Im w) in C/Z by the action of f+w.

The modulus of this torus is called the complex rotation number of f+w.

As the width of the annulus A_w tends to zero (Im w ->0), the limit values of the complex rotation number form a fractal set ``Bubbles'' related to the dynamics of a circle diffeomorphism f. I will discuss this relation, as well as shapes of bubbles and their self-similarity.