Approximately invariant manifolds and global dynamics of spike states |
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| Authors: | Peter W Bates Kening Lu Chongchun Zeng |
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| Institution: | (1) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;(2) Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;(3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA |
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| Abstract: | 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. |
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