×

Determining asymptotic behavior from the dynamics on attracting sets. (English) Zbl 0933.34059

Two tracking properties for trajectories on attracting sets are studied. The authors prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to another. A sufficient condition for asymptotic completeness of invariant exponential attractors is found, obtaining similar results as in the theory of inertial manifolds. Furthermore, such sets are shown to be retracts of the phase space, which implies that they are simply connected.

MSC:

34D45 Attractors of solutions to ordinary differential equations
34D35 Stability of manifolds of solutions to ordinary differential equations
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37B25 Stability of topological dynamical systems
34G20 Nonlinear differential equations in abstract spaces
PDFBibTeX XMLCite
Full Text: DOI