论文标题
对哈密顿二型的生成功能条形码的近似
Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms
论文作者
论文摘要
持久性模块和条形码用于符号拓扑中，以定义汉密尔顿二型不变性的各种不变性，但是计算这些条形码的数值方法尚未得到很好的发展。 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.
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.
