Invariant manifolds for analytic dynamical systems over ultrametric fields.

Abstract: We give an exposition of the theory of invariant manifolds around a fixed point, in the case of time-discrete, analytic dynamical systems over a complete ultrametric field . Typically, we consider an analytic manifold modelled on an ultrametric Banach space over , an analytic diffeomorphism , and a fixed point of . Under suitable assumptions on the tangent map , we construct a centre–stable manifold, a centre manifold, respectively, an -stable manifold around , for a given real number . [Copyright &y& Elsevier]