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:
caspian journal of mathematical sciencesPublisher: university of mazandaran
ISSN 1735-0611
volume 3
issue 2 2014
Keywords
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