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Talk abstract:
Normal form computations
in CONTENT
Yuri A. Kuznetsov, CWI/RIACA, Amsterdam
CONTENT is an interactive environment for detection, analysis, and
continuation of various bifurcations of ODEs, iterated maps, and
other dynamical systems. An important part of the analysis of local
bifurcations is the computation of their normal forms at the critical
parameter values. This means restricting the system to the corresponding
center manifold and then normalizing the system on the center manifold
by appropriate changes of variables, parameters, and time.
The algorithms used in CONTENT to compute numerically the coefficients of
the normal forms for
- fold,
- Hopf,
- cusp, and
- Bogdanov-Takens
bifurcations of ODEs, as well as for
- fold,
- flip, and
- Neimark-Sacker
bifurcations of iterated maps, will be presented in detail. An important
feature of these algorithms is that no preliminary transformation of the
linear part to the Jordan normal form is applied.
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