Symbolic dynamics and transfer operators for Weyl chamber flows: a class of examples

符号模型集的无序复杂度和熵

Amorphic complexity and entropy for symbolic model sets

本文研究了由模型集生成的子移位中Weyl伪度量的连续性，并利用此结果构建了展示不同熵、无序复杂度及其最大等连续因子行为的子移位。

Equidistribution and counting of periodic flat tori

Let $G$ be a semisimple Lie group without compact factor and $Γ< G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on maximal flat periodic tori of the space of Weyl chambers. We prove that these flat periodic tori equidistribute exponentially fast towards the quotient of the Haar measure. From the equidistribution formula, we deduce a higher rank prime geodesic theorem. These counting and equidistribution results also hold in the non cocompact, finite covolume case for $G=\mathrm{SL}(d,\mathbb{R})$ and $Γ<\mathrm{SL}(d,…

旗丛的Morse谱和Lyapunov谱及动力学

Morse and Lyapunov Spectra and Dynamics on Flag Bundles

本文研究了与旗丛上流的动力学有关的流的特征指数。出发点是具有半单群$G$的主丛上的流.针对Iwasawa分解的投影$G = KAN$定义了流上的加性上循环，其值在$\frak{a} = \log A$中。研究了它的李雅普诺夫指数（沿轨迹的极限）和Morse指数（沿链的极限）.证明了这些谱集的一个对称性，即在外尔群下的不变性.它还证明，这些集位于某些Weyl室，从相关的标志束的动态定义。作为特殊情况，考虑了向量丛上的线性流。

横向子群的真正间断作用、增长指标与共形测度

Properly discontinuous actions, growth indicators, and conformal measures for transverse subgroups

本文研究连通半单实代数群的横向子群，证明其在 Weyl chamber 流空间上的作用是真正间断的，定义了 Bowen-Margulis-Sullivan 测度，建立了遍历二分法，并引入增长指标扩展了 Quint 的工作。