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

2008/11/30 by Tomas Johnson, Warwick Tucker
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algorithm #Applied mathematics #Computation #Convergence (economics) #Geometry #Invariant (physics) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Numerical methods for differential equations #Pure mathematics #Quantum chaos and dynamical systems #Saddle #Saddle point #Taylor series #math.DS #msc:34C20 #msc:37D10 #msc:37M99 #msc:65G20

paper · pdf · doi:10.1007/s12346-011-0040-2

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

arxiv created 2010/01/24 · openalex publication_date 2011/02/01 · arxiv updated 2011/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Automated computation of robust normal forms of planar analytic vector fields
• A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
• A Rigorous ODE Solver and Smale’s 14th Problem
• Deterministic Nonperiodic Flow
• Invariant Manifolds