Polygonal approximation of flows
Polygonal approximation of flows
复制标题
流量的多边形近似
DOI：
10.1016/j.topol.2006.04.033
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
K. Mischaikow
中科院分区：
文献类型：
--
作者：
E. Boczko;W. Kalies;K. Mischaikow
对常微分方程产生的流动的定性行为的分析通常需要数值模拟之外的定量信息，而这些信息很难通过分析获得。在本文中，我们提出了一种计算方案，旨在利用康利指数理论的思想捕获定性信息。具体来说，我们从相空间的单纯分解中设计了一种组合多值近似，它可用于提取孤立不变集的孤立块。这些隔离块可以经过严格计算以提供计算机辅助证明。我们还获得了底层单纯近似的局部条件，保证了链循环集可以被很好地近似。
The analysis of the qualitative behavior of flows generated by ordinary differential equations often requires quantitative information beyond numerical simulation which can be difficult to obtain analytically. In this paper we present a computational scheme designed to capture qualitative information using ideas from the Conley index theory. Specifically we design an combinatorial multivalued approximation from a simplicial decomposition of the phase space, which can be used to extract isolating blocks for isolated invariant sets. These isolating blocks can be computed rigorously to provide computer-assisted proofs. We also obtain local conditions on the underlying simplicial approximation that guarantees that the chain recurrent set can be well-approximated.