On the Shape Conley Index Theory of Semiflows on Complete Metric Spaces
On the Shape Conley Index Theory of Semiflows on Complete Metric Spaces
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完备度量空间上半流的形状康利指数理论
DOI：
10.3934/dcds.2016.36.1629
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Jinqiao Duan
中科院分区：
文献类型：
--
作者：
Jintao Wang;Desheng Li;Jinqiao Duan
本文利用一个较弱的形指数对的概念，发展了完备度量空间上局部半流的形Conley指数理论。这使得我们能够通过将系统限制在包含K的局部不稳定流形的任何闭子集上来计算紧致孤立不变集K的形状指数，从而显著增加了形状指数和莫尔斯方程计算的灵活性。特别是，它允许计算形状指数和莫尔斯方程的无限维系统，通过使用不变集的不稳定流形，而不需要系统是双边的不稳定流形。
In this work we develop the shape Conley index theory for local semiflows on complete metric spaces by using a weaker notion of shape index pairs. This allows us to calculate the shape index of a compact isolated invariant set K by restricting the system on any closed subset that contains a local unstable manifold of K, and hence significantly increases the flexibility of the calculation of shape indices and Morse equations. In particular, it allows to calculate shape indices and Morse equations for an infinite dimensional system by using only the unstable manifolds of the invariant sets, without requiring the system to be two-sided on the unstable manifolds.