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...

discrete iterated function systems discrete iterated function systems representation of discrete sequences with dimensional discrete iterated function systems discrete iterated function systems stochastic discrete scale invariance: renormalization representation of discrete sequences with high-dimensional power domains and iterated function systems fractal tilings from iterated function systems...

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.

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

The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. The nondensity of OSP with respect to the C1-topology is proved. The proof uses the method of skew products developed by Ilyashenko and Gorodetskĭı.