Geometry and Ergodic Theory of Parabolic Meromorphic Functions

Abstract

Let f be a parabolic transcendental meromorphic function with positive and finite order rho and its derivative satisfies some growth conditions. In this paper, we show the existence of conformal measures and use this basic tool to illustrate both geometrical and dynamical features of the radial Julia set. We also characterize the conformal measures supported on radial Julia sets.