## Institute for Mathematical Sciences

## Preprint ims90-4

** A.E. Eremenko and M. Yu. Lyubich **
*Dynamical Properties of Some Classes of Entire Functions*

Abstract: The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.

View ims90-4 (PDF format)