论文标题
Integrodifference方程的数值动力学：$ l^p（ω）$中不变捆的层次结构
Numerical dynamics of integrodifference equations: Hierarchies of invariant bundles in $L^p(Ω)$
论文作者
论文摘要
我们研究了$ p $积分功能的BANACH空间上非自主综合差异方程的不变流形的“完整层次结构”如何在Galerkin类型的空间离散化下行为。这些歧管包括经典的稳定，中心稳定，中心，中心不稳定和不稳定的歧管，可以表示为$ c^m $ functions的图。对于具有平滑属性的内核，我们的主要结果在$ c^{m-1} $ - 拓扑中建立了这些图的亲密关系，该拓扑是在保留该方法收敛顺序的数值离散下。它是以定量方式制定的，从技术上讲，它是由对不变束存在的一般扰动定理（即\ \ \ nonanticous formolt歧管）所产生的。
We study how the "full hierarchy" of invariant manifolds for nonautonomous integrodifference equations on the Banach spaces of $p$-integrable functions behaves under spatial discretization of Galerkin type. These manifolds include the classical stable, center-stable, center, center-unstable and unstable ones, and can be represented as graphs of $C^m$-functions. For kernels with a smoothing property, our main result establishes closeness of these graphs in the $C^{m-1}$-topology under numerical discretizations preserving the convergence order of the method. It is formulated in a quantitative fashion and technically results from a general perturbation theorem on the existence of invariant bundles (i.e.\ nonautonomous invariant manifolds).
