Persistence of laminations

Persistence of stratification of normally expanded laminations

This manuscript complements the Hirsch-Pugh-Shub (HPS) theory on persistence of normally hyperbolic laminations and the theorem of Robinson on the structural stability of diffeomorphisms that satisfy Axiom A and the strong transversality condition (SA). We generalize these results by introducing a geometric object: the stratification of laminations. It is a stratification whose strata are lamin...

Persistence of stratifications of normally expanded laminations

We introduce here the concept of stratification of laminations. We explain also a sufficient condition which provides the C1persistence of a stratification of laminations preserved by a C1-endomorphism of a manifold. We present various applications of this result. To cite this article: P. Berger, C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Published by Elsevier Masson SAS on behalf of Aca...

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