Abstract
This paper studies behaviors that are defined on a torus, or equivalently, behaviors defined in spaces of periodic functions, and establishes their basic properties analogous to classical results of Malgrange, Palamodov, Oberst et al. for behaviors on $\mathbb{R}^n$. These properties—in particular the Nullstellensatz describing the Willems closure—are closely related to integral and rational points on affine algebraic varieties.
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