Computer Assisted Proof for Normally Hyperbolic Invariant Manifolds
Autor: | Capinski, Maciej J., Simo, Carles |
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Rok vydání: | 2011 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.1088/0951-7715/25/7/1997 |
Popis: | We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a non-rigorous, good enough, guess is necessary. The required assumptions are formulated in a way which allows for rigorous computer assisted verification. We apply our method for a driven logistic map, for which non-rigorous numerical simulation in plain double precision suggests the existence of a chaotic attractor. We prove that this numerical evidence is false and that the attractor is a normally hyperbolic invariant curve. Comment: 33 pages, 16 figures |
Databáze: | arXiv |
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