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

Abstract

Let $\phi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\phi$ and ${\phi }^{-1}$ admit absolute train track representatives. We prove that $\phi$ acts on the space of projectivized geodesic currents on $F_N$ with generalized uniform North-South dynamics.

v3, 35pp, 2 figures. Major revisions following reviewer's comments

References in corpus (4)

• North-South dynamics of hyperbolic free group automorphisms on the space of currents
• Perron-Frobenius theory and frequency convergence for reducible substitutions
• Graph towers, laminations and their invariant measures
• Long turns, INP's and index for free group automorphisms

Cited by in corpus (7)

• North-South dynamics of hyperbolic free group automorphisms on the space of currents
• Hyperbolic extensions of free groups from atoroidal ping-pong
• Perron-Frobenius theory and frequency convergence for reducible substitutions
• Atoroidal dynamics of subgroups of Out(F_N)
• Graph towers, laminations and their invariant measures
• Marked length pattern rigidity for arithmetic manifolds
• Train track maps for graphs of groups