Teichmüller动力学的Lagrange谱重整化
Lagrange Spectra in Teichmüller Dynamics via renormalization
摘要：
本文引入SL（2，R）在平移曲面的模空间上作用的闭不变轨迹的Lagrange谱，推广了经典的Lagrange谱，并利用重整化技术对它们进行了分析.根据Rauzy-Veech归纳法建立了这类谱的值的计算公式，并证明了任何不变轨迹都有闭合的Lagrange谱，且对应于伪Anosov元的值是稠密的.此外，我们表明，拉格朗日谱算术Teichmüller光盘包含霍尔射线，通过第二个公式，它使用经典的连分数算法给出了明确的限制。此外，我们证明了有界Teichmüller测地线和有界型区间交换变换的几种定义的等价性，并证明了Rauzy-Veech归纳法中关于模空间到边界的偏移的正矩阵范数的定量估计.
英文摘要：
We introduce Lagrange Spectra of closed-invariant loci for the action of SL(2,R) on the moduli space of translation surfaces, generalizing the classical Lagrange Spectrum, and we analyze them with renormalization techniques. A formula for the values in such spectra is established in terms of the Rauzy-Veech induction and it is used to show that any invariant locus has closed Lagrange spectrum and values corresponding to pseudo-Anosov elements are dense. Moreover we show that Lagrange spectra of arithmetic Teichmüller discs contain an Hall's ray, giving an explicit bound for it via a second formula which uses the classical continued fraction algorithm. In addition, we show the equivalence of several definitions of bounded Teichmüller geodesics and bounded type interval exchange transformations and we prove quantitative estimates on excursions to the boundary of moduli space in terms of norms of positive matrices in the Rauzy-Veech induction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
