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Invariant manifolds as pullback attractors of nonautonomous differential equations. (English) Zbl 1286.34068

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.

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

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