Veech风树模式计数问题中的定量误差项
Quantitative error term in the counting problem on Veech wind-tree models
摘要：
我们研究周期性风树模型，台球在平面上赋予$\mathbb{Z}^2$ -周期性位于相同的连接对称直角障碍。我们表现出有效的渐近公式的数量（合痕类）的周期台球轨迹（高达$\mathbb{Z}^2$ -翻译）的Veech风树台球，也就是说，风树台球的基础紧凑的翻译表面是Veech表面。我们表明，误差项取决于频谱特性的Veech组，并给出明确的估计的情况下，障碍物的边长平方$1/2$。
英文摘要：
We study periodic wind-tree models, billiards in the plane endowed with $\mathbb{Z}^2$-periodically located identical connected symmetric right-angled obstacles. We exhibit effective asymptotic formulas for the number of (isotopy classes of) periodic billiard trajectories (up to $\mathbb{Z}^2$-translations) on Veech wind-tree billiards, that is, wind-tree billiards whose underlying compact translation surfaces are Veech surfaces. We show that the error term depends on spectral properties of the Veech group and give explicit estimates in the case when obstacles are squares of side length $1/2$.
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