Related papers: A note on odometers and shadowing
In this article we characterize monotone extensions of cw-expansive homeomorphisms of compact metric spaces. We study the topology of its quotient space in the case of a compact surface. These results are applied to prove that there are…
We use Wagner's algorithm to estimate the number of periodic points of certain selfmaps on compact surfaces with boundary. When counting according to homotopy classes, we can use the asymptotic density to measure the size of sets of…
Accurate and robust global localization is essential to robotics applications. We propose a novel global localization method that employs the map traversability as a hidden observation. The resulting map-corrected odometry localization is…
For an $\alpha$-expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has…
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call…
In this note we study some properties of topological entropy for noncompact non-metrizable spaces.
This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular…
A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$. We show that any topological embedding of a circle into Euclidean $d$-space can have at most two shadows…
This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of…
We prove that if $T: X \to X$ is a selfmap of a set $X$ such that $\bigcap \{T^{n}X: n\in N}\}$ is a one-point set, then the set $X$ can be endowed with a compact Hausdorff topology so that $T$ is continuous.
We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.
For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal…
In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…
We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large…
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map $g$ which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map).…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the…
On any compact space one can consider the map which sends a point to the set of points farthest from this point. In nice cases, there is just a single point farthest from a given point and so by restricting the domain slightly one can form…
We can approximate a continuous self-map $f$ of a compact metric space by discretizing the space into a grid. Through either the map itself or a time series, $f$ induces a multivalued grid map $\mathcal F$. The dynamical properties of…
The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…