Abstract:

I am interested in studying the iteration of holomorphic self-maps of $mathbb C^*=mathbb Csetminus {0}$ for which both zero and infinity are essential singularities. I will describe the geometry of the logarithmic tracts for this class of functions and discuss about the notion of order of growth. In particular I will focus on the family $f(z) = z^m * exp( P(z) + Q(1/z) )$ where $P(z)$ and $Q(z)$ are polynomials and $m$ is an integer.