We show the existence of a distal dynamical system which possess an uncountable distributionally scrambled set of type 3. This distal system has no Li-Yorke pairs, hence the distributional chaos of type 3 does not imply the Li-Yorke chaos. Moreover, the system is conjugated to a system without any distributionally scrambled pair. Therefore the distributional chaos of type 3 is not preserved by ...

We investigate the prevalence of Li-Yorke pairs for C and C multimodal maps f with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If f is topologically mixing and has no Cantor attractor, then typical (...

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...

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 ...

The paper analyzes the structure and inner long-term dynamics of invariant compact sets for skewproduct flow induced by a family time-dependent ordinary differential equations nonhomogeneous linear dissipative type. main assumptions are made on term homogeneous equations. rich casuistic includes uniform stability sets, as well presence Li-Yorke chaos Auslander-Yorke inside attractor.