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

Tomas Johnson, Warwick Tucker

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15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)107-121
Number of pages15
JournalQualitative Theory of Dynamical Systems
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Dec 2011
Externally publishedYes

Keywords

  • Auto-validated numerics
  • Hyperbolic fixed points
  • Invariant manifolds
  • Normal forms

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