Nonunique Ergodicity on the Boundary of Outer space

Abstract

To an $\mathbb{R}$-tree in the boundary of Outer space, we associate two simplices: the simplex of projective length measures, and the simplex of projective dual currents. For both kinds of simplices, we estimate the dimension of maximal simplices for arational $\mathbb{R}$-trees in the boundary of Outer space.

44 pages, 9 figures. v2: Incorporated Referee's comments. To appear in Advances in Mathematics