Limit sets of unfolding paths in Outer space

TL;DR

This paper constructs a specific unfolding path in Outer space that accumulates on an entire simplex of measures on a non-geometric arational R-tree, revealing complex boundary behavior and dual ergodic currents.

Contribution

It introduces a novel unfolding path in Outer space with unique accumulation properties and characterizes the dual ergodic currents of the associated R-tree.

Findings

Unfolding path does not converge in the boundary of Outer space.

Path accumulates on the entire 1-simplex of projectivized length measures.

The R-tree admits exactly two dual ergodic projective currents.

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 non-geometric arational $\mathbb{R}$-tree T. We also show that T admits exactly two dual ergodic projective currents.