On almost specification and average shadowing properties

LIMIT AVERAGE SHADOWING AND DOMINATED SPLITTING

In this paper the notion of limit average shadowing property is introduced for diffeomorphisms on a compact smooth manifold M and a class of diffeomorphisms is given which has the limit average shadowing property, but does not have the shadowing property. Moreover, we prove that for a closed f-invariant set Lambda  of a diffeomorphism f, if Lambda is C1-stably limit average shadowing and t...

Almost specification ‎and ‎renewality‎ in spacing shifts

‎Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: ‎s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map‎. ‎We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points‎. ‎Moreover‎, ‎we show that if $h(sigma_P)=0$‎, ‎then $Sigma_...

On Bi-shadowing of Subclasses of Almost Contractive Type Mappings

A result on bi-shadowing for continuous single-valued contractions satisfying certain conditions has been given by AlBadarneh (2015). In this paper, we continue the discussion of asymptotic properties of trajectories for mappings belonging to more subclasses of almost contractions. In particular, we prove that Zamfirescu Mappings, QuasiContractions, Generalised Contractions, and Hardy-Rogers Co...

On ergodicity of systems with the asymptotic average shadowing property

The sequence asymptotic average shadowing property and transitivity

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...