A framework toward understanding the characterization of holomorphic dynamics
Keyword(s):
This chapter reviews the characterization of geometrically finite rational maps and then outlines a framework for characterizing holomorphic maps. Whereas Thurston's methods are based on estimates of hyperbolic distortion in hyperbolic geometry, the framework suggested here is based on controlling conformal distortion in 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 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.
2016 ◽
Vol 37
(6)
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pp. 1997-2016
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2000 ◽
Vol 75
(4)
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pp. 535-593
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2008 ◽
Vol 634
(6-7)
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pp. 1145-1148
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2005 ◽
Vol 178
(4)
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pp. 1017-1022
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2010 ◽
Vol 183
(3)
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pp. 451-516
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