, Volume 10, Issue 1, pp 107-121
Date: 02 Feb 2011

A Note on the Convergence of Parametrised Non-Resonant Invariant Manifolds

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Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.