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Ergodic currents dual to a real tree

Published online by Cambridge University Press:  12 November 2014

THIERRY COULBOIS  and
ARNAUD HILION
THIERRY COULBOIS
Affiliation:
Mathématiques, Université d’Aix-Marseille, Marseille, France email thierry.coulbois@univ-amu.fr, arnaud.hilion@univ-amu.fr
ARNAUD HILION
Affiliation:
Mathématiques, Université d’Aix-Marseille, Marseille, France email thierry.coulbois@univ-amu.fr, arnaud.hilion@univ-amu.fr
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Abstract

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 also give a unique ergodicity criterion.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 745 - 766
Copyright
© Cambridge University Press, 2014 

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