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.

中文翻译：

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外层空间展开路径的极限集

我们在外层空间构建一条展开路径，该路径不会在边界处收敛，而是在非几何无理数上的投影长度测量的整个 1-单纯形上累积 ${\mathbb R}$ -树时间。我们还表明时间恰好承认两个对偶遍历射影电流。这是无理树的第一个非几何例子，它既不是唯一遍历的，也不是唯一遍历的。