LI-YORKE CHAOTIC GENERALIZED SHIFT DYNAMICAL SYSTEMS

‎In this text we prove that in generalized shift dynamical system (XGamma,sigmavarphi)‎ ‎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 (XGamma,sigmavarphi) is‎ Li-Yorke chaotic;‎ - the dynamical system (XGamma,sigmavarphi) has‎ an scrambled pair;‎ ‎- the map varphi:GammatoGamma has at least‎ one non-quasi-periodic point‎.