Limit shadowing property

On shadowing: Ordinary and ergodic

“…It was developed intensively in recent years and became a significant part of dynamical systems containing a lot of deep connections to the notions of stability and chaotic behavior (e.g., [8,10,12,14]). Topological mixing and specification are two another formal ways to get some special dynamical properties and also chaos in global sense [2,11].…”

Symplectic diffeomorphisms with limit shadowing

“…From now on, we introduce the notions of the limit shadowing properties which were studied by [4,19,25,28]. We say that a sequence {x i } i∈Z is a limit pseudo…”

“…The shadowing property is very closely related to the stability theory. For this reason, various shadowing properties (shadowing [3,29,30], limit shadowing [4,6,8,14,18,19], inverse shadowing [9,13,26], orbital shadowing [10,16,27], average shadowing [11,12,21,24], ergodic shadowing [5,17,20], periodic shadowing [15], etc.) have been studied by many researchers.…”

Usual limit shadowable homoclinic classes of generic diffeomorphisms

“…Therefore, we study the some kinds of the shadowing property (usual limit shadowing property) and homoclinic classes. As to the research on the usual limit shadowing property, there exist [1,3,4]. We say that f has the usual limit shadowing property on Λ if for any sequence ξ = {x…”