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• W3100678712 abstract "We prove that every transcendental meromorphic map f with a disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question." @default.
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• W3100678712 date "2014-02-08" @default.
• W3100678712 modified "2023-09-27" @default.
• W3100678712 title "On the connectivity of the Julia sets of meromorphic functions" @default.
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• W3100678712 doi "https://doi.org/10.1007/s00222-014-0504-5" @default.
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