Laminations in Holomorphic Dynamics Mikhail Lyubich and Yair Minsky

Laminations in Holomorphic Dynamics

Conformal and Harmonic Measures on Laminations Associated with Rational Maps

The framework of aane and hyperbolic laminations provides a unifying foundation for many aspects of conformal dynamics and hyperbolic geometry. The central objects of this approach are an aane Riemann surface lamination A and the associated hyperbolic 3-lamination H endowed with an action of a discrete group of iso-morphisms. This action is properly discontinuous on H, which allows one to pass ...

On the classification of laminations associated to quadratic polynomials

Given any rational map f , there is a lamination by Riemann surfaces associated to f . Such laminations were constructed in general by Lyubich and Minsky. In this paper, we classify laminations associated to quadratic polynomials with periodic critical point. In particular, we prove that the topology of such laminations determines the combinatorics of the parameter. We also describe the topolog...

Tessellation and Lyubich-Minsky laminations associated with quadratic maps I: Pinching semiconjugacies

We introduce tessellation of the filled Julia sets for hyperbolic and parabolic quadratic maps. Then the dynamics inside their Julia sets are organized by tiles which work like external rays outside. We also construct continuous families of pinching semiconjugacies associated with hyperblic-to-parabolic degenerations without using quasiconformal deformation. Instead we use tessellation and inve...

Transcendental Ending Laminations

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν − , ν+). In this note, we show that there are ending laminations ν+ such that for any choice of ν − , the punctured torus group is transcendental as a subgroup of PSL2C.