This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li–Yorke and Wiggins ...

A new mathematical concept of abstract similarity is introduced and illustrated in the space infinite strings on a finite number symbols. The problem chaos presence for Sierpinski fractals, Koch curve, as well Cantor set solved by considering natural map. This accomplished Poincaré, Li-Yorke Devaney chaos, including multi-dimensional cases. Original numerical simula...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

Abstract This paper is concerned with the existence of chaos for a type partial difference equations. We establish four chaotification schemes equations tangent and cotangent functions, in which systems are shown to be chaotic sense Li–Yorke or both Devaney. For illustration, we provide three examples provided.

In this paper, the dynamics of elementary cellular automaton rule 41 is investigated in the bi-infinite symbolic sequence space. In spite of rule 41 is not surjective, but it possess of rich and complex dynamical behaviors. The existence of attractors and subshifts of finite type of the rule’s global map is strictly proved, some interesting dynamical properties on these subshifts, such as posit...

Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

We study the discrete dynamics of interval maps generated by action erasing block substitutions on binary expansion. propose a classification in hierarchy classes displaying progressively stronger character. investigate how this affects corresponding maps, showing that richest dynamical behavior (Devaney and Li-Yorke chaos, infinite topological entropy) is achieved at precise step hierarchy, wh...