North–South dynamics of hyperbolic free group automorphisms on the space of currents

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Let [Formula: see text] be a hyperbolic outer automorphism of a non-abelian free group [Formula: see text] such that [Formula: see text] and [Formula: see text] admit absolute train track representatives. We prove that [Formula: see text] acts on the space of projectivized geodesic currents on [Formula: see text] with generalized uniform North-South dynamics.