Rational solutions of first-order differential equations.
Covering properties of meromorphic functions, negative curvature and spherical geometry.
Sharp estimates for hyperbolic metrics and covering theorems of Landau type.
On the iteration of entire functions
Dynamical properties of some classes of entire functions
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.
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