Optimal low-dimensional dynamical approximations

Abstract

We present a method for determining optimal coordinates for the representation of an inertial manifold of a dynamical system. The condition of optimality is precisely defined and is shown to lead to a unique basis system. The method is applied to the Neumann and Dirichlet problems for the Ginzburg-Landau equation. Substantial reduction in the size of the dynamical system, without loss of accuracy is obtained from the method.