Practical normal form computations for vector fields

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...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Mechanik Vol. 84; no. 7; pp. 472 - 482
Main Authors Mayer, S., Scheurle, J., Walcher, S.
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag 01.07.2004
WILEY‐VCH Verlag
Wiley-VCH
Subjects
Exact sciences and technology
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Poincaré-Dulac normal form
reduced vector field
Sciences and techniques of general use
stability
Applied mechanics
Applied mathematics
Normal form
Eigenvalue
Hopf bifurcation
Vector field
Linearization
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Summary: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.
Bibliography:istex:FF8EC5B20A146EEE8296A0F8A40D99762B470FD3
ark:/67375/WNG-8TPN1ZT1-Z
ArticleID:ZAMM200310115
Supported in part by DFG‐Graduiertenkolleg “Hierarchie und Symmetrie in mathematischen Modellen” at RWTH Aachen
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.200310115