Hyperbolic-parabolic deformations of rational maps

Guizhen Cui (1) , Lei Tan (2)

1 Department of Engineering Mechanics
2 Department of Mechanical and Materials Engineering

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. * 2010 Mathematics Subject Classification: 37F20, 37F45 supported by NSFC grant no. 11125106.

Domaines: Systèmes dynamiques [math.DS]

Guizhen Cui, Lei Tan. Hyperbolic-parabolic deformations of rational maps . 2015. ⟨hal-01116673⟩