TY - JOUR
T1 - Practical normal form computations for vector fields
AU - Mayer, Sebastian
AU - Scheurle, Jürgen
AU - Welcher, Sebastian
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
KW - Poincaré-Dulac normal form
KW - Reduced vector field
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=3342914757&partnerID=8YFLogxK
U2 - 10.1002/zamm.200310115
DO - 10.1002/zamm.200310115
M3 - Article
AN - SCOPUS:3342914757
SN - 0044-2267
VL - 84
SP - 472
EP - 482
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
IS - 7
ER -