Invariant Measures for Univalent Self-Maps of the Unit Disc

We develop a translation-type model for univalent self-maps φ of the unit disc having an interior fixed-point and use the model to classify the φ-invariant measures on . We are particularly interested in maps which can be embedded in continuous semigroups of holomorphic self-maps of . Received: February 2, 2007. Revised: June 18, 2007. Accepted: July 4, 2007.