Floquet Theory and Stability of Periodic Solutions of Renewal Equations

Abstract

We prove the validity of a Floquet theory and the existence of Poincare maps for periodic solutions of renewal equations, also known as Volterra functional equations. Our approach is based on sun–star perturbation theory of dual semigroups and relies on a spectral isolation property and on the regularity of the semiflow. This contributes a new chapter to the stability analysis, in analogy with ordinary and retarded functional differential equations as well as the case of equilibria.