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arXiv:1612.04424 [math.DS]AbstractReferencesReviewsResources

A positive characterization of rational maps

Dylan P. Thurston

Published 2016-12-13Version 1

When is a topological branched self-cover of the sphere equivalent to a rational map on CP^1? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive criterion: the branched self-cover is equivalent to a rational map if and only if there is an elastic spine that gets "looser" under backwards iteration. This completes a series announced in arXiv:1502.02561 and started in arXiv:1507.05294 and arXiv:1607.00340.

Comments: 32 pages, 6 figures
Categories: math.DS, math.CV
Subjects: 37F10, 37E25, 37F30
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