Computer assisted proof for normally hyperbolic invariant manifolds

Maciej J Capiński, Carles Simó
2012 Nonlinearity  
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
more » ... 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.
doi:10.1088/0951-7715/25/7/1997 fatcat:2zmrwescb5bixfwbx2auasvovi