Related papers: A note on shadowing properties

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…

Let $L$ be a proper differentiation invariant subspace of $C^\infty(a,b)$ such that the restriction operator $\frac{d}{dx}\bigl{|}_L$ has a discrete spectrum $\Lambda$ (counting with multiplicities). We prove that $L$ is spanned by…

Let $(X,G,\Phi)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property,…

Constant mean curvature (CMC) surfaces in space forms can be described by their associated $\mathbb C^*$-family of flat $SL(2,\mathbb C)$-connections $\nabla^\lambda$. In this paper we consider the asymptotic behavior (for $\lambda\to0$) of…

We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such…

Let M be a closed, symplectic connected Riemannian manifold, f a symplectomorphism on M. We prove that if f is C1-stably weakly shadowing on M, then the whole manifold M admits a partially hyperbolic splitting.

Let $f\colon X\to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is onto. Using this we go on to show that, for expansive…

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.

In this paper, we will show that any geometric Lorenz flow in a definite class satisfies the parameter-shifted shadowing property.

We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing…

We prove that for all metric spaces $X$ the following properties of the lamplighter space $\mathsf{La}(X)$ are equivalent: (1) $\mathsf{La}(X)$ has finite Nagata dimension, (2) $\mathsf{La}(X)$ has Markov type 2, (3) $\mathsf{La}(X)$ does…

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…

It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…

We construct a locally compact Hausdorff topology on the path space of a finitely aligned $k$-graph $\Lambda$. We identify the boundary-path space $\partial\Lambda$ as the spectrum of a commutative $C^*$-subalgebra $D_\Lambda$ of…

We show that Lorenz flows have neither limit shadowing property nor average shadowing property nor the asymptotic average shadowing property where the reparametrizations related to these concepts relies on the set of increasing…

Let $X$ be a topological space admitting an amenable cover of multiplicity $k\in\mathbb{N}$. We show that, for every $n\geq k$ and every $\alpha\in H_n(X;\mathbb{R})$, the image of $\alpha$ in the $\ell^1$-homology module…

In this paper we extend to an infinite dimensional setting some results on the shadowing property that are known on finite dimensional compact manifolds without border and in $\mathbb{R}^n$. In fact, we show that if $\{\T(t):t\ge 0\}$ is a…

If $G$ is a complex simply connected semisimple algebraic group and if $\lambda$ is a dominant weight, we consider the compactification $X_\lambda$ in the projectivisation of $\End(V(\lambda))$ obtained as the closure of the $G\times…

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…

The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a…