# Ergodic currents dual to a real tree

@article{Coulbois2014ErgodicCD, title={Ergodic currents dual to a real tree}, author={Thierry Coulbois and Arnaud Hilion}, journal={Ergodic Theory and Dynamical Systems}, year={2014}, volume={36}, pages={745 - 766} }

Let $T$ be an $\mathbb{R}$-tree with dense orbits in the boundary of outer space. When the free group $\mathbb{F}_{N}$ 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 ${\it\mu}$ dual to $T$, the unfolding induction produces a sequence of approximations converging towards ${\it\mu}$. We…

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