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A finiteness theorem for a dynamical class of entire functions. (English) Zbl 0657.58011

We define a class \(\Sigma\) of entire functions whose covering properties are similar to those of rational maps. The set \(\Sigma\) is closed under composition of functions, and we show that when regarded as dynamical systems of the plane, the elements of \(\Sigma\) share many properties with rational maps. In particular, they have finite dimensional spaces of quasiconformal deformations, and they contain no wandering domains in their stable sets.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37C75 Stability theory for smooth dynamical systems
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References:

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