Combinatorial characterization of sub-hyperbolic rational maps
نویسندگان
چکیده
In 1980’s, Thurston established a combinatorial characterization for post-critically finite rational maps among post-critically finite branched coverings of the two sphere to itself. A completed proof was written by Douady and Hubbard in their paper [A. Douady, J.H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993) 263–297]. This criterion was then extended by Cui, Jiang, and Sullivan to sub-hyperbolic rational maps among sub-hyperbolic semi-rational branched coverings of the two sphere to itself. The goal of this paper is to present a new but simpler proof for the combinatorial characterization of sub-hyperbolic rational maps by adapting some arguments in the proof in Douady and Hubbard’s paper. © 2009 Elsevier Inc. All rights reserved. MSC: 58F23; 30D05
منابع مشابه
Thurston Type Theorem for Sub-hyperbolic Rational Maps
In 1980’s, Thurston established a combinatorial characterization for post-critically finite rational maps. This criterion was then extended by Cui, Jiang, and Sullivan to sub-hyperbolic rational maps. The goal of this paper is to present a new but simpler proof of this result by adapting the argument in the proof of Thurston’s Theorem.
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