不可可积系统的定量行为（IV）
Quantitative behavior of non-integrable systems (IV)
摘要：
本文分为两个部分。在第七节中，我们简化了任意有限多边形平移曲面的基于特征值的剩余短线方法。这使得确定某些无限轨道的无规则指数变得简单得多，并且可以更快地找到某些无限模型中某些轨道到无穷大的逃逸率。在第8节中，我们的主要目标是扩展剩余短线方法，无论是基于特征值的版本，以及特征值的版本，应用到一个大类的2-维平面动力系统超出polysquare，包括所有的Veech表面，并建立时间定量的等分布和时间定量的超密度的一些无限轨道在这些新的系统。
英文摘要：
In this paper, there are two sections. In Section 7, we simplify the eigenvalue-based surplus shortline method for arbitrary finite polysquare translation surfaces. This makes it substantially simpler to determine the irregularity exponents of some infinite orbits, and quicker to find the escape rate to infinity of some orbits in some infinite models. In Section 8, our primary goal is to extend the surplus shortline method, both this eigenvalue-based version as well as the eigenvalue-free version, for application to a large class of 2-dimensional flat dynamical systems beyond polysquares, including all Veech surfaces, and establish time-quantitative equidistribution and time-quantitative superdensity of some infinite orbits in these new systems.
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。
