We use the shadowing approach to study the long-time behavior of numerical approximations of semilinear parabolic equations. We show that the corresponding nonlinear semigroup has a Lipschitz shadowing property in a neighborhood of its global attractor. The proof is based on reduction to an inertial manifold and application of shadowing techniques developed for nite-dimensional systems. When ap...

Scaffolding and shadowing techniques have been shown to improve language learners’ reading comprehension. However, little attention has been paid to the comparative effectiveness of these techniques. This study investigated the effect of three selected scaffolding techniques (peer scaffolding, distributed scaffolding, and reciprocal scaffolding) versus three types of shadowing (complete shadowi...

We describe the limit sets in affine control systems, in affine differential systems with impulses. In contrast with the fixed points in ODE case, these sets may have a fractal structure. We give estimations of their Hausdorff dimension. For these systems we extend the notion of Shadowing Property and state this property in the neighborhoods of the attractors and repellers in control systems.

Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, ultrametric complete spaces. We develop theory shifts type for infinite alphabets. call them order. the basic shadowing property in general metric spaces, exhibiting similarities differences with compact connect these two theories setting zero-dimensional showing th...

We study continuous maps of the unit interval into itself We determine necessary and su cient conditions so that all pseudo orbits can be approximated by orbits with the same initial point

We show that if a volume-preserving diffeomorphism belongs to the C1-interior of the set of all volume preserving diffeomorphisms having the periodic shadowing property then it is Anosov. Mathematics Subject Classification: 37C10, 37C50, 37D20

We introduce various new type of recurrent sets for finitely generated semigroups on non-compact metric spaces that are conjugacy invariant, and obtain some basic properties chain via these definitions. Moreover, we define the notion weak shadowing property group actions compact spaces, which is weaker than property, prove equivalence a generalized homogeneous space without isolated points.

The theory of zero-dimensional extensions is a useful tool in the study entropy theory. In present paper, we aim to which properties can be preserved by suitable extension. For dynamical system ( X , G ? ) prove that shadowing property implies it factor inverse limit subshifts with property. Moreover, if totally disconnected, extension conjugate. Besides, transitivity (or mixng) mixng, respecti...

We show that an invertible bilateral weighted shift is strongly structurally stable if and only it has the shadowing property. also exhibit a K{o}the sequence space supporting frequently hypercyclic shift, but no chaotic shifts.

We show that if a diffeomorphism has the periodic shadowing property on the chain recurrent set, then the closure of the periodic set is the chain recurrent set. Mathematics Subject Classification: 37C50