2008/10/29 by Tomas Johnson, Warwick Tucker · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algorithm #Applied mathematics #Computation #Computer science #Flow (mathematics) #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Normal #Numerical Methods and Algorithms #Planar #Polynomial and algebraic computation #Saddle #Saddle point #Transformation (genetics) #Vector field #math.DS #msc:34C20 #msc:37M99 #msc:65G20 #msc:65L70
paper · pdf · doi:10.3934/dcdsb.2009.12.769
published as Discrete and continuous dynamical systems - Series B 12(4):769-782 (2009).
arxiv created 2008/10/29 · openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighbourhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method.