Patterson–Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space

Ilya Kapovich (1) , Martin Lustig (2)

1 Department of Mathematics [Urbana]
2 I2M - Institut de Mathématiques de Marseille

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.

Mots clés: Culler–Vogtmann's outer space; Patterson–Sullivan measures; geodesic currents

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]

Ilya Kapovich, Martin Lustig. Patterson–Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space. Pacific Journal of Mathematics, 2015, 277 (2), pp.371--398. ⟨10.2140/pjm.2015.277.371⟩. ⟨hal-01318444⟩