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Hyperbolic-parabolic deformations of rational maps

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arxiv 1501.01385 v3 pith:XFXETV6V submitted 2015-01-07 math.DS

Guizhen Cui , Lei Tan This is my paper · ORCID
classification math.DS
keywords rationalmapspinchingconvergesdeformationsfinitegeometricallypath
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We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.

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Cited by 1 Pith paper

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  1. The landing of parameter rays at non-recurrent critical portraits

    math.DS 2019-08 reject novelty 6.0 of 10

    Every parameter ray at a critical portrait of a degree-d (d≥2) non-recurrent polynomial lands at that polynomial.

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