Slowly divergent geodesics in moduli space

发散测地线、歧义闭测地线与二元加性除数问题

Divergent geodesics, ambiguous closed geodesics and the binary additive divisor problem

本文研究负曲率局部对称空间中发散测地线间的公共垂线计数，给出非纯指数增长的渐近公式，并应用于模轨道流形中歧义测地线的计数，恢复Sarnak结果并证实推广Motohashi猜想。

A divergent Teichmuller geodesic with uniquely ergodic vertical foliation

We construct an example of a quadratic differential whose vertical foliation is uniquely ergodic and such that the Teichmuller geodesic determined by the quadratic differential diverges in the moduli space of Riemann surfaces.

Divergent on average directions of Teichmuller geodesic flow

The set of directions from a quadratic differential that diverge on average under Teichmuller geodesic flow has Hausdorff dimension exactly equal to one-half.

负曲率中发散测地线的等分布

Equidistribution of divergent geodesics in negative curvature

本文研究非紧有限体积负曲率流形及几何有限树商空间中的发散测地线，证明其随复杂度增大分别趋向最大熵测度与 Bowen–Margulis 测度等分布。

Hausdorff dimension of divergent diagonal geodesics on product of finite volume hyperbolic spaces

In this article, we consider the product space of several non-compact finite volume hyperbolic spaces, $V_1, V_2, \dots , V_k$ of dimension $n$. Let $\mathrm{T}^1(V_i)$ denote the unit tangent bundle of $V_i$ for each $i=1,\dots , k$, then for every $(v_1, \dots , v_k) \in \mathrm{T}^1 (V_1) \times \cdots \times \mathrm{T}^1 (V_k)$, the diagonal geodesic flow $g_t$ is defined by $g_t (v_1, \dots , v_k) = (g_t v_1, \dots , g_t v_k)$. And we define $$\mathfrak{D}_k =\left\{ (v_1, \dots, v_k) \in \mathrm{T}^1 (V_1) \times \cdots \times \mathrm{T}^1 (V_k): g_t(v_1, \dots, v_k) \text{ divergent, as…

\(R^2\)中加权奇异向量的缓慢发散轨迹

Slowly Divergent Trajectories for Weighted Singular Vectors in R^2

研究\(R^2\)中加权奇异向量，证明满足特定条件的\(w\) - 奇异向量集豪斯多夫维数为\(s_w = 2 - (1 + w_1)^{-1}\)。对不同参数给出加权均匀逼近集维数，用自仿射构造等方法直接证明下包络定理。