Related papers: Parameterized IFS with the asymptotic average shad…
We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering set consisting of the finite number of critical elements (i.e., singularities or closed orbits).…
We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
We prove that when $f$ is a continuous selfmap acting on compact metric space $(X,d)$ which satisfies the shadowing property, then the set of irregular points (i.e. points with divergent Birkhoff averages) has full entropy. Using this fact…
In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of the functions, but we do not assume any separation condition.…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
In this paper, we explore a topological system $f:M\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\subseteq\mathcal {M}_{inv}(f)$ coincides with…
We explore the notion of two-sided limit shadowing property introduced by Pilyugin \cite{P1}. Indeed, we characterize the $C^1$-interior of the set of diffeomorphisms with such a property on closed manifolds as the set of transitive Anosov…
Let $M$ be a smooth compact manifold and $\Lambda$ be a compact invariant set. In this paper we prove that for every robustly transitive set $\Lambda$, $f|_\Lambda$ satisfies a $C^1-$generic-stable shadowable property (resp.,…
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space.…
We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space has the limit shadowing property, then the restriction of $f$ to the non-wandering…
Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…
In this paper we study the asymptotic behavior of linear processes having as innovations mean zero, square integrable functions of stationary reversible Markov chains. In doing so we shall preserve the generality of coefficients assuming…
We discuss whether classical examples of dynamical systems satisfying the shadowing property also satisfy the shadowing property for the induced map on the hyperspace of continua, obtaining both positive and negative results. We prove that…
We study the metric mean dimension of $\Phi$-irregular set $I_{\Phi}(f)$ in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class $Y$, the values…
This paper relates - for point processes $\Phi$ on $\mathbb{R}$ - two types of asymptotic mean stationarity (AMS) properties and several absolute continuity results for the common probability measures emerging from point process theory. It…
In this paper we investigate the asymptotic statistical theory of irreducible quantum Markov chains, focusing on identifiability properties and asymptotic convergence of associated quantum statistical models. We show that the space of…
We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…
We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the $C^1$-interior of the set of all diffeomorphisms having so-called inverse periodic…
Discrete-time birth-death processes may or may not have certain properties known as asymptotic aperiodicity and the strong ratio limit property. In all cases known to us a suitably normalized process having one property also possesses the…