Periodic behaviors

2010/01/13 by Diego Napp, Napp, Diego, Marius van der Put +3
Mathematics · #35B10 #35E20 #93B25 #93C05 #93C20 #93C35 #Commutative Algebra (math.AC) #FOS: Mathematics #Optimization and Control (math.OC) #math.AC #math.OC #msc:35B10 #msc:35E20 #msc:93B25 #msc:93C05 #msc:93C20 #msc:93C35

paper · pdf · doi:10.48550/arxiv.1001.2255

13 pages

arxiv created 2010/07/30 · arxiv updated 2010/08/02

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

Related

• Good Reduction of Periodic Points
• Rational points in periodic analytic sets and the Manin-Mumford conjecture
• Periodic points, linearizing maps, and the dynamical Mordell-Lang problem
• Representation of quasi-periodic functions and Hausdorff-Young inequalities for Besicovitch almost periodic functions
• Periodic binary harmonic functions