Smooth Linearization of Nonautonomous Coupled Systems
Abstract
In a joint work with Palmer we have formulated sufficient conditions under which there exist continuous and invertible transformations of the form Hn(x,y) taking solutions of a coupled system equation* xn+1 =Anxn+fn(xn, yn), yn+1=gn( yn), equation* onto the solutions of the associated partially linearized uncoupled system equation* xn+1 =Anxn, yn+1=gn( yn). equation* In the present work we go one step further and provide conditions under which Hn and Hn-1 are smooth in one of the variables x and y. We emphasise that our conditions are of a general form and do not involve any kind of dichotomy, nonresonance or spectral gap assumptions for the linear part which are present on most of the related works.
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