Dynamics of meromorphic Misiurewicz maps.
Abstract. Properties of meromorphic transcendental maps of the Riemann sphere will be discussed. Several key theorems known for rational maps still hold in this case.
However, an important difference exists in the criterion for the existence of a probabilistic absolutely continuous invariant measure, which in the transcendental case requires an additional hypothesis about the essential singularity at infinity. This condition can be expressed in terms of the Nevanlinna characteristic of the function. (joint work with J. Kotus)