F. Ayatollah Zadeh Shirazi - Faculty of Math., Stat. and Computer Science, College of Science, University of Tehran, Tehran, Iran
J. Nazarian Sarkooh - Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

‎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.

Generalized shift, Li-Yorke chaos, Scrambled pair