Invariant manifolds for finite-dimensional non-archimedean dynamical systems

Abstract

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.

v2: minor revisions, 25 pages. The preprint is based on unpublished parts of the author's preprint arXiv:0808.2709 [math.DS]