Related papers: Syndetic proximality and scrambled sets

Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal.,…

In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a…

In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…

We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase…

In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transitive and are not locally equicontinuous.

Here we survey on the growth of systoles of arithmetic locally symmetric spaces under the congruence covering and give simple proofs for the best possible constants of Gromov for several important classes of symmetric spaces.

This paper is concerning to the geometric study of fixed points of a self-mapping on a metric space. We establish new generalized contractive conditions which ensure that a self-mapping has a fixed disc or a fixed circle. We introduce the…

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was…

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…

This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…

Given a compact metric space $X$ and an upper semicontinuous function $F\colon X \to 2^X$, we explore the dynamic system $(X,F)$. In this study, we introduce new concepts, demonstrate various results, and provide numerous examples. In…

Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…

We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…

The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…

In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is…

The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…

We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric…

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of…

We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.