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- W2226797 abstract "This chapter contains the main proof of persistence of noncompact normally hyperbolic invariant manifolds. We first state both the trivial bundle and general version of the main theorem and discuss these in full detail. We include a precise comparison with results in the literature, followed by an outline of the proof. Then we discuss the differences to the compact case and present detailed examples to illustrate these. To start the actual proof, we first prepare the system: we put it in a suitable form and obtain estimates for the perturbed system. Then we prove that there exists a unique persistent invariant manifold and that it is Lipschitz. Secondly, we set up an elaborate scheme in to prove that this manifold is smooth by induction over the smoothness degree." @default.
- W2226797 created "2016-06-24" @default.
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- W2226797 date "2013-01-01" @default.
- W2226797 modified "2023-09-25" @default.
- W2226797 title "Persistence of Noncompact NHIMs" @default.
- W2226797 doi "https://doi.org/10.2991/978-94-6239-003-4_3" @default.
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