Computer Assisted Proof for Normally Hyperbolic Invariant Manifolds

Autor:	Capinski, Maciej J., Simo, Carles
Rok vydání:	2011
Předmět:	Mathematics - Dynamical Systems
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
Externí odkaz:	http://arxiv.org/abs/1105.1277 Zobrazit plný text záznamu View this record from Arxiv