Hyperbolic-parabolic deformations of rational maps
Hyperbolic-parabolic deformations of rational maps
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DOI：
10.1007/s11425-018-9426-4
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发表时间：
2015-01
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影响因子：
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通讯作者：
G. Cui;L. Tan
中科院分区：
文献类型：
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作者：
G. Cui;L. Tan
我们发展了一个Thurston类理论来刻画几何上有限的有理映射，然后应用它来研究有理映射的pinching和plumbing变形。证明了在一定条件下，从原映射到极限，拼挤路径一致收敛，拟共形共轭一致收敛到半共轭。相反，每一个具有抛物线点的几何有限有理映射都是任何指定的管道组合的收缩路径的着陆点。
We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under 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.