A completely analytical family of dynamical models for spherical galaxies and bulges with a central black hole

We present a family of spherical models for elliptical galaxies and bulges consisting of a stellar component and a central black hole. All models in this family share the same stellar density profile, which has a steep central cusp. The gravitational potential of each models is a linear combination of the potential generated selfconsistently by the stars and the potential of a central black hole. The relative importance of these two contributions is a free parameter in the models. Assuming an isotropic dynamical structure, almost all kinematical properties of these models can be calculated analytically. In particular, they form the first simple dynamical models for galaxies with a central black hole where the distribution function and differential energy distribution can be written completely in terms of elementary functions only. We also present various extensions of this family to models with anisotropic orbital structures. Also for these dynamical models, the distribution function and its moments can be expressed completely in terms of elementary functions. This family is useful for a large range of applications, in particular to generate initial conditions for N-body and hydrodynamical simulations to model galactic nuclei with a central black hole.Comment: 13 pages, 1 figure, accepted for publication in MNRA

Iteration of meromorphic functions

This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).Comment: 38 pages. Abstract added in migration. See http://analysis.math.uni-kiel.de/bergweiler/ for recent comments and correction