Abstract:
In this paper the algebraic properties of the deterministic processes with dynamic represented by a homogeneous linear recurrence over the field $\mathbb{C}$ are studied. It is started with an overview of homogeneous linear recurrent processes over $\mathbb{C}$ and its subsets. Next, it is gone deeper into homogeneous linear recurrent processes over numerical rings. After that, the recurrence criteria over sign-based ring subsets are analyzed. Also, the deterministic processes with dynamic represented by a Littlewood, Newman or Borwein homogeneous linear recurrence are considered.
Keywords and phrases:dynamical process; homogeneous linear recurrence; characteristic polynomial; Littlewood, Newman and Borwein recurrences.
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