相关论文: Mean Ergodic Shadowing

An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a…

We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…

This paper examines the relationship between shadowing phenomena and the continuity properties of $\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower)…

In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…

Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices…

In this paper, we introduce the concept of quasi-semi hyperbolic pseudo-orbits and prove that quasi-semi hyperbolicity implies quasi hyperbolicity provided the error magnitude are sufficiently small. We also have successively demonstrated…

We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…

We prove that for finitely generated free semigroup actions the average shadowing property, the weak asymptotic average shadowing property, the mean ergodic shadowing property, the almost asymptotic average shadowing property, the…

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stronger than might initially seem. We give some implications of…

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…

We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.

The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…

We investigate a shadowing property which appears naturally in the study of piecewise monotonic maps of the interval. It turns out to be a weak form of the rank one property, a well-known notion in abstract ergodic theory. We show that this…

In previous papers we define certain Lagrangian shadows of ample divisors in algebraic varieties. In the present brief note an existence condition is discussed for these Lagrangian shadows.

We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the…

We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…

In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and…