Abstract:

In this talk we will be concerned with some one complex dimensional slices of parameter spaces transcendental meromorphic maps. Properties of components of these slices are controlled by the singularities of the functions. Components in which the functions have attracting cycles that attract a critical point are often "Mandelbrot-like" whereas those that attract an asymptotic value are quite different and have a shell-like appearance. These appears, for example, in the family of tangent maps. In this talk we will describe these Shell components.