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