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We show that a nonautonomous discrete-time dynamical system (NDS) with the ergodic shadowing property is chain mixing. As a result, it is obtained that a k-periodic NDS with the ergodic shadowing property has the shadowing property. In particular, any k-periodic NDS on intervals having the ergodic shadowing is Devaney chaotic. Additionally, we prove that for an equicontinuous NDS with the shadowing property, the notions of topologically mixing, pseudo-orbital specification, weak specification property, and ergodic shadowing property are equivalent. [ABSTRACT FROM AUTHOR]

Abstract In this paper we introduce a concept of weak stability for non-autonomous dynamical systems. We characterize the set of weak stable points and show that the set of weak stable points is residual, and investigate the relation between weak stability and shadowing property. We also discuss the relation between weak stability of a non-autonomous dynamical system and its induced set-valued system. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new notion, named controlled shadowing property and we relate it to some notions in dynamical systems such as topological ergodicity, topologically mixing and specification properties. The relation between the controlled shadowing and chaos in sense of Li-Yorke is studied. At the end we give some examples to investigate the controlled shadowing property. [ABSTRACT FROM AUTHOR]

In this paper we consider shadowing and weak shadowing properties for iterated function systems IFS and give some results on these concepts. At first, a sufficient condition for shadowing property is given and by this result we present two IFS which have the shadowing property. It is proved that every uniformly expanding as well as every uniformly contracting IFS has the weak shadowing property. By an example we show that in IFS's shadowing property does not imply weak shadowing property. Finally we have the main result of the paper and prove that the weak shadowing is a generic property in the set of all IFS's. [ABSTRACT FROM AUTHOR]

We say that a dynamical system X has the Ramsey shadowing property if an arbitrary sequence of points in X can be shadowed on a set that is "large" in the sense of Ramsey theory. Our main theorem states that this property is equivalent to the existence of a dense set of minimal points. [ABSTRACT FROM AUTHOR]

It is proved that a nontrivial compact dynamical system with asymptotic average shadowing property (AASP) displays uniformly distributional chaos or distributional chaos in a sequence. Moreover, distributional chaos in a system with AASP can be uniform and dense in the measure center, that is, there is an uncountable uniformly distributionally scrambled set consisting of such points that the orbit closure of every point contains the measure center. As a corollary, the similar results hold for the system with almost specification property. [ABSTRACT FROM AUTHOR]

Using the shadowing property of the dynamical system, we prove the generalized HyersUlam stability of quintic functional equations. [ABSTRACT FROM AUTHOR]

We study the effect of radio signal shadowing dynamics, caused by vehicles and by buildings, on the performance of beaconing protocols in Inter-Vehicular Communication (IVC). Recent research indicates that beaconing, i.e., one hop message broadcast, shows excellent characteristics and can outperform other communication approaches for both safety and efficiency applications, which require low latency and wide area information dissemination, respectively. To mitigate the broadcast storm problem, adaptive beaconing solutions have been proposed and designed. We show how shadowing dynamics of moving obstacles hurt IVC, reducing the performance of beaconing protocols. To the best of our knowledge, this is one of the first studies on identifying the problem and the underlying challenges and proposing the opportunities presented by such challenges. Shadowing also limits the risk of overloading the wireless channel. We demonstrate how these challenges and opportunities can be taken into account and outline a novel approach to dynamic beaconing. It provides low-latency communication (i.e., very short beaconing intervals), while ensuring not to overload the wireless channel. The presented simulation results substantiate our theoretical considerations. [ABSTRACT FROM AUTHOR]

Let ${\it\gamma}$ be a hyperbolic closed orbit of a $C^{1}$ vector field $X$ on a compact $C^{\infty }$ manifold $M$ and let $H_{X}({\it\gamma})$ be the homoclinic class of $X$ containing ${\it\gamma}$. In this paper, we prove that if a $C^{1}$-persistently expansive homoclinic class $H_{X}({\it\gamma})$ has the shadowing property, then $H_{X}({\it\gamma})$ is hyperbolic. [ABSTRACT FROM AUTHOR]