Shift dynamical systems over finite fields
Abstract: A trajectory over the finite field is a function from the integers I to . The set of all trajectories over is a topological vector space in the product topology induced by the discrete topology on , and coordinatewise addition and scalar multiplication of trajectories. Let be a continuous linear operator on which commutes with the shift. If x is a trajectory over , then the -orbit of x is the sequence of trajectories . Suppose that is not a scalar multiple of the identity. Theorem. The trajectory x is periodic if and only if the -orbit of x is eventually periodic.
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Keywords: Shift dynamical systems, symbolic flows, periodic trajectories, periodic orbits, sequence spaces
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