Hyperbolic-parabolic deformations of rational maps Dedicated to the Memory of Professor Lei Tan  

作　　者：Guizhen Cui Lei Tan 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences [2]LAREMA, Université d'Angers

出　　处：《Science China Mathematics》2018年第12期2157-2220,共64页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11125106)

摘　　要：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.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.

关 键 词：rational map geometrically finite HYPERBOLIC PARABOLIC 

分 类 号：O1[理学—数学]