Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
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.
