Computer assisted proof for normally hyperbolic invariant manifolds

被引:20
作者
Capinski, Maciej J. [1 ]
Simo, Carles [2 ]
机构
[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
[2] Univ Barcelona, Dept Matemat Aplicada & Anal, E-08007 Barcelona, Spain
关键词
COVERING RELATIONS; CONE CONDITIONS; CHAOS; ATTRACTORS; EXISTENCE;
D O I
10.1088/0951-7715/25/7/1997
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 an 'a posteriori' verification by rigorous-interval-based numerical analysis. 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.
引用
收藏
页码:1997 / 2026
页数:30
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