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.
Complex rotation numbers and bubbles
19.03.2021 16:30 - 17:30
Organiser:
H. Bruin, R. Zweimüller
Location:
zoom-meeting