Related papers: A type of shadowing and distributional chaos
This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
For a continuous self-map of a star graph to be Li-Yorke chaotic and to have full periodicity, we prove some new sufficient conditions on the orbit of the center.
The main aim of this article is to show that maps with specification property have invariant distributionally scrambled sets and that this kind of scrambled set can be transferred from factor to extension under finite-to-one factor maps.…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…
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…
The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our…
This paper is concerned with strong Li-Yorke chaos induced by A-coupled-expansion for time-varying (i.e., nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li-Yorke are established via strict…
Transmission of the scalar field through the random medium, represented by the system of randomly distributed dielectric cylinders is calculated numerically. System is mapped to the problem of electronic transport in disordered…
We define shadowable points for homeomorphism on metric spaces. In the compact case we will prove the following results: The set of shadowable points is invariant, possibly nonempty or noncompact. A homeomorphism has the pseudo-orbit…
A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random…
Let K denote a compact invariant set for a strongly monotone semiflow in an ordered Banach space E, satisfying standard smoothness and compactness assumptions. Suppose the semiflow restricted to K is chain transitive. The main result is…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincar\'e map of simple two-dimensional discrete time piecewise linear systems involving a…
We study in detail the trajectories followed by single images during binary microlensing events. Starting from perturbative resolutions of the lens equation, we explore the full parameter space by continuity arguments. We see that the…
In this paper, we introduce the definitions of periodic point, transitivity, sensitivity and Devaney chaos of multiple mappings from a set-valued perspective. We study the relation between multiple mappings and its continuous self-maps and…