On Some Properties of the Shift on an Infinite-Dimensional Torus

We study the question, classical in the theory of dynamical systems, about the minimalityof the shift on an infinite-dimensional torus; more precisely, the problem of finding sufficientconditions guaranteeing the absence of the minimality property is solved.

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In this study, we solve a classical problem in the theory of dynamical systems regarding the minimality of the shift on an infinite-dimensional torus. More specifically, we provide sufficient conditions that guarantee the absence of the minimality property.