Related papers: Syndetic proximality and scrambled sets

A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…

We consider two categories related to symplectic manifolds: 1. Objects are symplectic manifolds and morphisms are symplectic embeddings. 2. Objects are symplectic manifolds endowed with compatible almost complex structure and morphisms are…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

We study the dynamics in the neighborhood of fixed points in a 4D symplectic map by means of the color and rotation method. We compare the results with the corresponding cases encountered in galactic type potentials and we find that they…

We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…

A novel type of self-organized lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic…

This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…

We answer the two questions left open in [Z.~Ko\v{c}an, Internat. J. Bifur. Chaos Appl. Sci. Engrg. \textbf{22}, article id: 125025 (2012)] i.e. whether there is a relation between $\omega$-chaos and distributional chaos and whether there…

We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…

We describe some of the important physical characteristics of the `pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-scale self-assembly occurs. We highlight the fact that there exist features of self-assembly…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps…

The main aim of this paper is extending the concept of scambled pair and Li--Yorke chaos to non--uniform compact dynamical systems. We show for finite (compact Alexandroff) topological space $X$ with at least two elements the following…

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a…

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called {\it…

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…

In this note, we introduce a new approach to abstract ``synthetic'' projective lines. We discuss various aspects of our approach, and compare these aspects with the classical one. A number of intriguing questions arise. Amongst these…

Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…