  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 R^n. These properties - in particular the Nullstellensatz
describing the Willems closure - are closely related to integral and rational
points on affine algebraic varieties.
