Yuefei Wang

On the dynamics of composite entire functions

Letf andg be nonlinear entire functions. The relations between the dynamics off⊗g andg⊗f are discussed. Denote byℐ (·) andF(·) the Julia and Fatou sets. It is proved that ifz∈C, thenz∈ℐ8464 (f⊗g) if and only ifg(z)∈ℐ8464 (g⊗f); ifU is a component ofF(f○g) andV is the component ofF(g○g) that containsg(U), thenU is wandering if and only ifV is wandering; ifU is periodic, then so isV and moreover,V is of the same type according to the classification of periodic components asU. These results are used to show that certain new classes of entire functions do not have wandering domains.

Transformations and non-degenerate maps

AbstractWe shall prove the equivalences of a non-degenerate circle-preserving map and a Möbius transformation in

Non-linear differential equations with transcendental meromorphic solutions

\hat {\mathbb{R}}^n

Sharp forms of nevanlinna’s error terms

, of a non-degenerate geodesic-preserving map and an isometry in ℍn, of a non-degenerate line-preserving map and an affine transformation in ℝn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

Periodic points and normal families concerning multiplicity

Completely invariant components of the Fatou sets of meromorphic maps are discussed. Positive answers are given to Baker’s and Bergweiler’s problems that such components are the only Fatou components for certain classes of meromorphic maps.

The pointwise convergence of p-adic Möbius maps

In this paper we treat two non-linear differential equations which come from complex dynamics theory. We give a complete classification of the equations when they possess transcendental meromorphic solutions.

Boundedness of Fatou Components of Holomorphic Maps

It is shown that meromorphic solutions of certain first-order nonlinear differential equations do not have wandering domains.

Isometries in hyperbolic spaces

AbstractLet f(z) be a meromorphic function in the plane. If ψ(t)/t andp(t) are two positive, continuous and non-decreasing functions on [1,∞) with ∫1∞dt/ψ(t) = ∞ and ∫1∞dt/p(t) = ∞, then