关于三维流形上唯一遍历向量场的一个观察

非唯一遍历代数树的构造

Constructing non-uniquely ergodic arational trees

在这个技术说明中，我们采用Gabai的思想来构造非唯一遍历的、非几何的、非理性的树。

唯一遍历算子的集合是路连通的

The set of uniquely ergodic IETs is path-connected

令$π$是至少$4$符号上的非退化置换。证明了具有置换$π$的唯一遍历区间交换变换的集合是路径连通的.

Path-connectivity of the set of uniquely ergodic and cobounded foliations

We show that for a closed surface of genus at least 5, or a surface of genus at least 2 with at least one marked point, the set of uniquely ergodic foliations and the set of cobounded foliations is path-connected and locally path-connected.

Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations

We construct Weil-Petersson (WP) geodesic rays with minimal filling non-uniquely ergodic ending lamination which are recurrent to a compact subset of the moduli space of Riemann surfaces. This construction shows that an analogue of the Masur's criterion for Teichmüller geodesics does not hold for WP geodesics.

具有极小非唯一遍历垂面叶理的Teichmüller测地线的极限集

Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation

我们描述了一种方法，用于构建Teichmüller测地线的垂直测量叶理$ν$是最小的，但不是唯一遍历，我们有一个很好的理解的Teichmüller测地线的行为。的建设取决于各种参数，我们表明，可以调整参数，以确保在瑟斯顿边界这样一个测地线的积累点的集合正是所有可能的测量叶理的同伦类的$ν$。进一步调整参数，甚至可以把$ν$看作是非唯一遍历叶理上的遍历测度。

On the Unique Ergodicity of Quadratic Differentials and the Orientation Double Cover

We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second theorem generalizes a result of Treviño for the horizontal flow on a translation surface, as well as Masur's criterion for unique ergodicity of the horizontal foliation.