论文标题
双曲线3空间中的台球编码
Coding of billiards in hyperbolic 3-space
论文作者
论文摘要
在本文中，我们扩展了符号动力学的范围，以在3维双曲空间中涵盖特定类别的理想多面体，这标志着在非欧洲裔空间中探索动态系统的重要一步。在台球动力学的背景下，我们为这些理想的多面体构建了一个新颖的编码系统，从而将它们的状态和时间空间离散为符号表示。本文通过建立尖台轨迹的空间与代码的相关偏移空间之间建立共轭来区分自己。这里的一个关键发现是，相关偏移空间的封闭是作为有限类型（SFT）的亚缩短出现的，阐明了这些系统的结构方面和渐近行为。
In this paper, we extend the scope of symbolic dynamics to encompass a specific class of ideal polyhedrons in the 3-dimensional hyperbolic space, marking an important step forward in the exploration of dynamical systems in non-Euclidean spaces. Within the context of billiard dynamics, we construct a novel coding system for these ideal polyhedrons, thereby discretizing their state and time space into symbolic representations. This paper distinguishes itself through the establishment of a conjugacy between the space of pointed billiard trajectories and the associated shift space of codes. A crucial finding herein is the observation that the closure of the related shift space emerges as a subshift of finite type (SFT), elucidating the structural aspects and asymptotic behaviour of these systems.
