标题： 顶点和边替换系统的极限空间 显示英文标题

标题： Limit spaces of vertex and edge replacement systems

摘要： 我们引入并研究VERSs（顶点和边替换系统）作为一种图扩展技术。 我们考虑其历史图，一个记录每次图扩展的增强树，并提供在何种情况下它是双曲的充分条件。 当它是双曲时，其Gromov边界就是我们所谓的VERS的极限空间。 我们提供了来自数学不同领域的三个例子：有限生成收缩自相似群的Schreier图和极限空间，单射的临界后有限迭代函数系统以及边替换系统的极限空间。 显示英文摘要

摘要： We introduce and study VERSs (vertex and edge replacement systems) as a technology of graph expansions. We consider its history graph, an augmented tree that records each graph expansion, and we provide sufficient conditions under which it is hyperbolic. When hyperbolic, its Gromov boundary is what we call the limit space of the VERS. We provide three examples from different areas of mathematics: Schreier graphs and limit spaces of finitely generated contracting self-similar groups, injective post-critically finite iterated function systems and limit spaces of edge replacement systems.