Aulbach, Bernd.; Rasmussen, Martin; Siegmund, Stefan Invariant manifolds as pullback attractors of nonautonomous differential equations. (English) Zbl 1286.34068 Discrete Contin. Dyn. Syst. 15, No. 2, 579-596 (2006). Summary: We discuss the relationship between invariant manifolds of nonautonomous differential equations and pullback attractors. This relationship is essential, e.g., for the numerical approximation of these manifolds. In the first step, we show that the unstable manifold is the pullback attractor of the differential equation. The main result says that every (hyperbolic or nonhyperbolic) invariant manifold is the pullback attractor of a related system which we construct explicitly using spectral transformations. To illustrate our theorem, we present an application to the Lorenz system and approximate numerically the stable as well as the strong stable manifold of the origin. Cited in 6 Documents MSC: 34C45 Invariant manifolds for ordinary differential equations 34D45 Attractors of solutions to ordinary differential equations 37D10 Invariant manifold theory for dynamical systems 37C60 Nonautonomous smooth dynamical systems Keywords:nonautonomous differential equation; pullback attractor; invariant manifold; numerical approximation. Software:GAIO PDFBibTeX XMLCite \textit{Bernd. Aulbach} et al., Discrete Contin. Dyn. Syst. 15, No. 2, 579--596 (2006; Zbl 1286.34068) Full Text: DOI