The Ontario Research Centre for Computer Algebra
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We present a method to compute center manifolds for dynamical
systems ${\bf \dot{x}} = {\bf f}({\bf x}, \mu), ({\bf x} \in {\bf
R}^n,
\mu \in {\bf R}^p)$,
where $x$ is a vector of state variables and $\mu$ is a vector of
parameters. Explicit formulae are derived and implemented in
Maple. This enables one to compute center manifolds to any order
easily. We also show how to analyze the errors of the analytical
approximations, and how they depend on the parameters, by
computing the \textsl{residual} or \textsl{defect}. Several
examples are given to show the applicability of the program.
This method should be of interest to the Computer Algebra
community as a testbed for several different sets of Computer
Algebra tools, namely transformations, linear algebra, and series.
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