Reduction principle at work

摘要

The purpose of this informal paper is three-fold: First,lling a gap in the literature, we provide a (necessary and sucient) principle of linearized stability for nonautonomous dierence equations in Banach spaces based on the dichotomy spectrum.Second, complementing the above, we survey and exemplify an ambient nonautonomous and innite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations.Third, these results are applied to integrodierence equations of Hammerstein- and Urysohn-type both in C- and L p -spaces.Specic features of the nonautonomous case are underlined.Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.