Every parameter ray at a critical portrait of a degree-d (d≥2) non-recurrent polynomial lands at that polynomial.
Hyperbolic-parabolic deformations of rational maps
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abstract
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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2019 1verdicts
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The landing of parameter rays at non-recurrent critical portraits
Every parameter ray at a critical portrait of a degree-d (d≥2) non-recurrent polynomial lands at that polynomial.