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.

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.

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...

Let X be a compact metric space and f be a continuous map from X into itself. In this paper, we introduce the concept of the sequence asymptotic average shadowing property, which is a generalization of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence asymptotic average shadowing property and investigate the relationship between the sequence asym...