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arXiv · 1302.3766

Ergodic currents dual to a real tree

Thierry Coulbois·Arnaud Hilion
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Abstract

Let $T$ be an $\R$-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 $\R$-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.

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Thierry Coulbois, Arnaud Hilion. 2013-02-15. Ergodic currents dual to a real tree. https://doi.org/10.1017/etds.2014.78

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