Approximately invariant manifolds and global dynamics of spike states

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• 作者：Peter W. Bates ; Kening Lu and Chongchun Zeng
• 刊名：Inventiones Mathematicae
• 出版年：2008
• 出版时间：November, 2008
• 年：2008
• 卷：174
• 期：2
• 页码：355-433
• 全文大小：825.2 KB

文摘

We investigate the existence of a true invariant manifold given an approximately invariant manifold for an infinite-dimensional dynamical system. We prove that if the given manifold is approximately invariant and approximately normally hyperbolic, then the dynamical system has a true invariant manifold nearby. We apply this result to reveal the global dynamics of boundary spike states for the generalized Allen–Cahn equation.