  Let M be an analytic manifold modelled on an ultrametric Banach space over a
complete ultrametric field. Let f be an analytic diffeomorphism from M onto
itself and p be a fixed point of f. We discuss invariant manifolds around p,
like stable manifolds, centre-stable manifolds and centre manifolds, with an
emphasis on results specific to the case that M has finite dimension. The
results have applications in the theory of Lie groups over totally disconnected
local fields.
