Bounded Geometry and Families of Meromorphic Functions with Two Asymptotic Values

Mathematics – Dynamical Systems

Scientific paper

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20 pages, 1 figure

Scientific paper

In this paper we consider the topological class, denoted by AV2, of universal
covering maps from the plane to the sphere with two removed points. We prove
that an element f in AV2 with finite post-singular set is combinatorially
equivalent to a meromorphic transcendental map g with constant Schwarzian
derivative if any only if f satisfies a Bounded Geometry condition.

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