Limit sets of Teichm"uller geodesics with minimal non-uniquely ergodic vertical foliation
Limit sets of Teichm"uller geodesics with minimal non-uniquely ergodic vertical foliation
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具有最小非唯一遍历垂直叶理的 Teichm"uller 测地线的极限集
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Kasra Rafi
中科院分区：
文献类型：
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作者：
C. Leininger;Anna Lenzhen;Kasra Rafi
我们描述了一种构造 Teichm"uller 测地线的方法，其中垂直测量的叶理 $
u$ 是最小的，但不是唯一遍历的，并且我们对 Teichm"uller 测地线的行为有很好的理解。该构造取决于各种参数，我们表明可以调整参数以确保瑟斯顿边界中此类测地线的累积点集合恰好是 $ 同伦类中所有可能测量的叶状结构的集合
u$。通过进一步调整参数，甚至可以将 $
u$ 是非唯一遍历叶状结构的遍历测度。
We describe a method for constructing Teichm"uller geodesics where the vertical measured foliation $
u$ is minimal but is not uniquely ergodic and where we have a good understanding of the behavior of the Teichm"uller geodesic. The construction depends on various parameters, and we show that one can adjust the parameters to ensure that the set of accumulation points of such a geodesic in the Thurston boundary is exactly the set of all possible measured foliations in the homotopy class of $
u$. With further adjustment of the parameters, one can even take $
u$ to be an ergodic measure on a non-uniquely ergodic foliation.