Preprint des Projektes: DFG Forschergruppe Spektrale Analysis, asymptotische Verteilungen und stochastische Prozesse

Numerische Approximation und Spektrale Analysis unendlich-dimensionaler Dynamischer Systeme

01-007 Sergei Pilyugin, A.A. Rodionova, K. Sakai.
Orbital and weak shadowing properties

We study weak and orbital shadowing properties of dynamical systems related to the following approach: we look for exact trajectories lying in small neighborhoods of approximate ones (or containing approximate ones in their small neigborhoods) or for exact trajectories such that the Hausdorff distances between their closures and closures of approximate trajectories are small. These properties are characterized for linear diffeomorphisms. We also study some C1-open sets of diffeomorphisms defined in terms of these prop- erties. It is shown that the C1-interior of the set of diffeomorphisms having the orbital shadowing property coincides with the set of structurally stable diffeomorphisms.