Periodic linear discrete multitime diagonal recurrence with application in economics

Abstract: Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet multipliers). The Floquet point of view brings about an important simplification: the initial linear diagonal recurrence system is reduced to a linear recurrence system, with constant coefficients along "diagonal lines". The results are applied to the discrete multitime Samuelson-Hicks models, with constant, respectively multi-periodic, coefficients, in order to find bivariate sequences with economic meaning. For constant coefficients case, it was found also the generating function; for multi-periodic coefficients case, we determined the Floquet multipliers.