论文标题
通过延续和持久性跟踪动力特征
Tracking Dynamical Features via Continuation and Persistence
论文作者
论文摘要
由于其在计算方法中使用的潜力，多生物场和组合动力系统最近已成为感兴趣的主题。在本文中，我们开发了一种方法，以跟踪一系列多生物场的隔离不变集（组合动力系统的显着特征）。通过在组合环境中置于孤立的不变设置的“延续”的经典概念来实现此目标。特别是，我们给出了一个“跟踪协议”，当给定一个种子孤立的不变集时，它会在一系列多生物场中找到种子的规范延续。如果不可能继续下去，我们将展示如何使用曲折的持久性跟踪与孤立不变集相关的同源特征。这种施工允许将继续视为持久性的特殊情况。
Multivector fields and combinatorial dynamical systems have recently become a subject of interest due to their potential for use in computational methods. In this paper, we develop a method to track an isolated invariant set -- a salient feature of a combinatorial dynamical system -- across a sequence of multivector fields. This goal is attained by placing the classical notion of the "continuation" of an isolated invariant set in the combinatorial setting. In particular, we give a "Tracking Protocol" that, when given a seed isolated invariant set, finds a canonical continuation of the seed across a sequence of multivector fields. In cases where it is not possible to continue, we show how to use zigzag persistence to track homological features associated with the isolated invariant sets. This construction permits viewing continuation as a special case of persistence.
