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

TL;DR

This paper introduces an a posteriori method to determine the convergence radii and error bounds of analytic parametrizations of non-resonant local invariant manifolds, enhancing numerical and theoretical analysis.

Contribution

It provides a novel approach to estimate convergence and errors of truncated series representations of invariant manifolds in dynamical systems.

Findings

Computed convergence radii for invariant manifolds

Provided error estimates for truncated series

Enabled local enclosures and existence proofs

Abstract

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.