Quantifying Transversality by Measuring the Robustness of Intersections
Quantifying Transversality by Measuring the Robustness of Intersections
复制标题
通过测量交叉点的稳健性来量化横向性
DOI：
10.1007/s10208-011-9090-8
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发表时间：
2009
影响因子：
3
通讯作者：
A. Patel
中科院分区：
文献类型：
--
作者：
H. Edelsbrunner;D. Morozov;A. Patel
根据定义，横向交叉口在无限小的扰动下是稳定的。利用持久同调，我们将这一概念扩展到一种度量。给定一个扰动空间，我们给交集的每一个同调类赋予它的稳健性，以及在这个空间中一个扰动的大小是杀死它所必需的，然后我们证明了健壮性是稳定的。这一结果的应用包括连续映射不动点的稳健性的稳定概念和光滑映射的轮廓线的稳定性的陈述。
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its robustness, the magnitude of a perturbation in this space necessary to kill it, and then we prove that the robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for contours of smooth mappings.