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For every irreducible hyperbolic automorphism φ 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  + (φ) is obtained as ‘diagonal closure’ of the support of the backward limit current μ − (φ). 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  + (φ), in terms of Bestvina–Feighn–Handel's ‘stable lamination’ associated to φ.

INVARIANT LAMINATIONS FOR IRREDUCIBLE AUTOMORPHISMS OF FREE GROUPS