Ergodic currents dual to a real tree

Abstract

Let $T$ be an $\mathbb{R}$-tree in the boundary of Outer space with dense orbits. When the free group $\FN$ acts freely on $T$, we prove that the number of projective classes of ergodic currents dual to $T$ is bounded above by $3N-5$. We combine Rips induction and splitting induction to define unfolding induction for such an $\mathbb{R}$-tree $T$. Given a current $\mu$ dual to $T$, the unfolding induction produces a sequence of approximations converging towards $\mu$. We also give a unique ergodicity criterion.

14 pages, minor corrections from previous version

Cited by in corpus (2)

• Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space
• Limit sets of unfolding paths in Outer space