  Consider briefly the equations of fluid dynamics-they describe the enormous
wealth of detail in all the interacting physical elements of a fluid
flow-whereas in applications we want to deal with a description of just that
which is interesting. In a wide variety of situations, simple approximate
models are needed to perform practical simulations and make forecasts. I review
the derivation, from a mathematical description of the detailed dynamics, of
accurate, complete and useful low-dimensional models of the interesting
dynamics in a system. The development of centre manifold theory and associated
techniques puts this modelling process on a firm basis. As in Guckenheinmer &
Holmes (1983,S2.5):
  "... these new methods will really be conventional perturbation style
analyses interpreted geometrically..."
  But the geometric viewpoint of dynamical systems theory greatly enriches our
approach by providing a rationale for also deriving correct initial conditions,
forcing and boundary conditions for the models-all essential elements of a
model.
