Laminations géodésiques plates

R-trees and laminations for free groups I: Algebraic laminations

This paper is the first of a sequence of three papers, where the concept of an Rtree dual to (the lift to the universal covering of) a measured geodesic lamination L in a hyperbolic surface S is generalized to arbitrary R-trees provided with a (very small) action of the free group FN of finite rank N ≥ 2 by isometries. In [CHL-II] to any such R-tree T a dual algebraic lamination L(T ) is associ...

Non-euclidean Affine Laminations

The purpose of the present paper is to discuss examples of aane Riemann surface laminations which do not admit a leafwise Euclidean structure. The rst example of such a lamination was constructed by Ghys Gh97]. Our discussion is based on the geometric methods developed by Lyubich, Minsky and the author LM97], KL01], which rely on the observation that any aane surface A gives rise in a natural w...

Laminations in Holomorphic Dynamics

Non-degenerate Quadratic Laminations

We give a combinatorial criterion for a critical diameter to be compatible with a nondegenerate quadratic lamination.

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.