LI-YORKE CHAOTIC GENERALIZED SHIFT DYNAMICAL SYSTEMS

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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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Journal title

volume 3  issue 2

pages  289- 295

publication date 2014-12-31

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