Ergodic currents dual to a real tree Auteur(s): Coulbois T., Hilion A.
Ref HAL: hal-01066575_v1 Ref Arxiv: 1302.3766 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: 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. Commentaires: 14 pages, minor corrections from previous version |