Abstract
Abstract
We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational
${\mathbb R}$
-tree T. We also show that T admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.
Funder
National Science Foundation
Alfred P. Sloan Foundation
Publisher
Cambridge University Press (CUP)
Reference43 articles.
1. Non-unique ergodicity, observers' topology and the dual algebraic lamination for $\Bbb R$-trees
2. [BF94] Bestvina, M. and Feighn, M. , ‘Outer limits’, Preprint, 1994, https://www.math.utah.edu/~bestvina/eprints/bestvina.feighn..outer_limits.pdf.
3. Intersection Form, Laminations and Currents on Free Groups
4. [Pau95] Paulin, F. , ‘De la géométrie et la dynamique des groupes discrets’, Habilitation á diriger les recherches, E.N.S. Lyon 6 (1995).