English

Ergodic currents dual to a real tree

Group Theory 2019-02-20 v2 Dynamical Systems

Abstract

Let TT be an R\R-tree in the boundary of Outer space with dense orbits. When the free group \FN\FN acts freely on TT, we prove that the number of projective classes of ergodic currents dual to TT is bounded above by 3N53N-5. We combine Rips induction and splitting induction to define unfolding induction for such an R\R-tree TT. Given a current μ\mu dual to TT, the unfolding induction produces a sequence of approximations converging towards μ\mu. We also give a unique ergodicity criterion.

Keywords

Cite

@article{arxiv.1302.3766,
  title  = {Ergodic currents dual to a real tree},
  author = {Thierry Coulbois and Arnaud Hilion},
  journal= {arXiv preprint arXiv:1302.3766},
  year   = {2019}
}

Comments

14 pages, minor corrections from previous version

R2 v1 2026-06-21T23:26:55.944Z