Approximately invariant manifolds and global dynamics of spike states
- First Online:
- Cite this article as:
- Bates, P., Lu, K. & Zeng, C. Invent. math. (2008) 174: 355. doi:10.1007/s00222-008-0141-y
- 278 Downloads
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.