Practical normal form computations for vector fields

Sebastian Mayer, Jürgen Scheurle, Sebastian Welcher

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We present a method to compute a Poincaré-Dulac normal form of a vector field, as well as a corresponding reduced vector field, near a stationary point with arbitrary linearization. Explicit knowledge of the eigenvalues of the linearization is not necessary, and only rational operations are required. Some examples are presented, including a normal form computation relevant for Hopf bifurcations, and coupled nonlinear oscillators.

Original languageEnglish
Pages (from-to)472-482
Number of pages11
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume84
Issue number7
DOIs
StatePublished - 2004

Keywords

  • Poincaré-Dulac normal form
  • Reduced vector field
  • Stability

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