Abstract
We give a topological characterization of rational maps with disconnected Julia sets. Our results extend Thurston’s characterization of postcritically finite rational maps. In place of iteration on Teichmüller space, we use quasiconformal surgery and Thurston’s original result.
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The first author is supported by the grants no. 10831004 and no. 10721061 of NNSF of China, and by Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences; the second author is supported by the EU Research Training Network on Conformal Structures and Dynamics.
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Cui, G., Tan, L. A characterization of hyperbolic rational maps. Invent. math. 183, 451–516 (2011). https://doi.org/10.1007/s00222-010-0281-8
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DOI: https://doi.org/10.1007/s00222-010-0281-8