A note on the convergence of parametrised non-resonant invariant manifolds

Details A note on the convergence of parametrised non-resonant invariant manifolds A note on the convergence of parametrised non-resonant invariant manifolds

2008-11-27

arxiv.org/abs/0811.4500v3

Qualitative Theory of Dynamical Systems 10(1):107-121 (2011)

Mathematics

Dynamical Systems

Scientific paper

10.1007/s12346-011-0040-2

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.

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