Persistence modules and barcodes are used in symplectic topology to define various invariants of Hamiltonian diffeomorphisms, however numerical methods for computing these barcodes are not yet well developed. In this paper we define one such invariant called the generating function barcode of compactly supported Hamiltonian diffeomorphisms of \( \mathbb {R}^{2n}\) by applying Morse theory to generating functions quadratic at infinity associated to such Hamiltonian diffeomorphisms and provide an algorithm (i.e a finite sequence of explicit calculation steps) that approximates it.

中文翻译：

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哈密​​顿微分同胚生成函数条码的近似

持久性模块和条形码在辛拓扑中用于定义哈密顿微分同胚的各种不变量，但是计算这些条形码的数值方法尚未得到很好的开发。在本文中，我们通过应用莫尔斯理论来生成与此类哈密顿微分同胚相关的无穷远二次函数，定义了一个这样的不变量，称为\ ( \mathbb {R}^{2n}\)的紧支持哈密顿微分同胚的生成函数条形码，并提供了近似它的算法（即显式计算步骤的有限序列）。