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A. Steindl, H. Troger:
"Dimension reduction: A key concept in dynamics";
Talk: 6th EUROMECH Conference ENOC 2008, St. Petersburg, Russia; 2008-06-30 - 2008-07-04; in: "Proceedings ENOC 2008", A. Fradkov (ed.); (2008), 5 pages.

The main idea in dimension reduction is the separation
of the variables into essential or active modes and
into ignorable or passive modes. However, it would
be a mistake to assume that the ignorable modes, can
be completely ignored in the derivation of the reduced
system. Due to nonlinear coupling the elimination of
these passive modes is a delicate matter. If these modes
are completely ignored in the calculation of the reduced
system the so-called standard (linear or flat) Galerkin
method, mostly used in engineering, is obtained. However,
this approach sometimes gives qualitatively incorrect
results and hence better strategies must be looked
for. Hence the representation of the passive modes by
means of the active modes is the essential step in applying
more sophisticated dimension reduction methods.
This is done in almost all different approaches by
invariant manifolds.

Center Manifolds, Nonlinear Galerkin Method, Condensation