1
Faculty of Math., Stat. and Computer Science, College of Science, University of Tehran, Tehran, Iran
2
Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Abstract
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 scrambled pair; - the map $varphi:GammatoGamma$ has at least one non-quasi-periodic point.
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