<p style='text-indent:20px;'>We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as structural space dynamical systems. We also that, this spaces, in order to determine whether system has shadowing, it sufficient check <i>continuously generated</i> pseudo-orbits shadowed.</p>

Let X = {a}∪ {ai | i ∈ N} be a subspace of Euclidean space E such that limi→∞ ai = a and ai 6= aj for i 6= j. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y ) of all homeomorphisms on Y , where Y = {a, b} ∪ {...

In this paper, the chaotic behavior of a set-valued mapping F : X → 2 , where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2 is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F , it is shown that the Bernoulli s...

We show that shadowing is a generic property among continuous maps and surjections on large class of locally connected one-dimensional dynamical systems.

We prove that small nonlinear perturbations of random linear dynamics admitting a tempered exponential dichotomy have version the shadowing property. As consequence, if is uniform, Hyer