Invariant laminations for irreducible automorphisms of free groups

For every irreducible hyperbolic automorphism ℓ of F N (i.e. the analog of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree T + (ℓ) is obtained as ' diagonal closure' of the support of the backward limit current μ - (ℓ). This diagonal closure is obtained through a finite procedure analogous to adding diagonal leaves from the complementary components to the stable lamination of a pseudo-Anosov homeomorphism. We also give several new characterizations as well as a structure theorem for the dual lamination of T + (ℓ), in terms of Bestvina-Feighn-Handel's ' stable lamination' associated to ℓ.