  We present a modern proof of some extensions of the celebrated
Hirsch-Pugh-Shub theorem on persistence of normally hyperbolic compact
laminations. Our extensions consist of allowing the dynamics to be an
endomorphism, of considering the complex analytic case and of allowing the
laminations to be non compact. To study the analytic case, we use the formalism
of deformations of complex structures. We present various persistent complex
laminations which appear in dynamics of several complex variables: Henon maps,
fibered holomorphic maps... In order to proof the persistence theorems, we
construct a laminar structure on the stable and unstable of the normally
hyperbolic laminations.
