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Abstract: |
In this talk, I will outline a framework for characterizing holomorphic dynamics. Whereas Thurston's methods are based on estimates of hyperbolic distortion in the hyperbolic geometry, the framework suggested here is based on controlling conformal distortion in the spherical geometry. The new framework enables one to relax two of Thurston's assumptions, first, that the iterated map has finite degree and, second, that its post critical set is finite. Thus, it makes it possible to characterize certain rational maps for which the post critical set is not finite as well as certain classes of entire and meromorphic coverings for which the iterated map has infinite degree. |
