论文标题
在地图和时间序列的网格分辨率上的摩尔斯分解的持续存在
Persistence of Morse decompositions over grid resolution for maps and time series
论文作者
论文摘要
我们可以通过将空间离散到网格中来近似紧凑的度量空间的连续自动图$ f $。通过地图本身或时间序列，$ f $诱导了一个多估计的网格地图$ \ Mathcal f $。 $ \ Mathcal F $的动力学属性取决于网格的分辨率，我们在更改分辨率时研究了这些属性的持久性。特别是，我们使用几个持久性的概念 - 图形结构，持久同源性和混合属性来查看摩尔斯分解的持久性，即全局（Morse图）和局部（单个Morse集）级别。
We can approximate a continuous self-map $f$ of a compact metric space by discretizing the space into a grid. Through either the map itself or a time series, $f$ induces a multivalued grid map $\mathcal F$. The dynamical properties of $\mathcal F$ depend on the resolution of the grid, and we study the persistence of these properties as we change the resolution. In particular, we look at the persistence of Morse decompositions, at both the global (Morse graph) and local (individual Morse set) levels, using several notions of persistence -- graph structure, persistent homology, and mixing properties.
