Invariant manifolds for analytic dynamical systems over ultrametric fields

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 KK. Typically, we consider an analytic manifold MM modelled on an ultrametric Banach space over KK, an analytic diffeomorphism f:M→Mf:M→M, and a fixed point pp of ff. Under suitable assumptions on the tangent map Tp(f)Tp(f), we construct a centre–stable manifold, a centre manifold, respectively, an aa-stable manifold around  pp, for a given real number a∈]0,1].