A computational approach to center manifolds is presented in this paper. The theory of center manifolds offers a way to reduce the dimension of a system of ordinary differential equations. In a series of theorems, the authors describe conditions on the coefficients of the system for the existence of particular trajectories and points on the center manifold; this is important when investigating the bifurcation behavior of such a system.

The paper focuses on center manifolds of a particular 3D system of differential equations. The system of equations is linear up to a correction term. Particular conditions on the linear part guarantee the existence of center manifolds for such a system. To find such conditions, the authors switch to a computational approach, and describe their investigations using the computer algebra systems Mathematica and Singular.

The computational approach to this theory is worth reading about, and is well described. The authors did a nice job focusing on the mathematical aspects, rather than just providing computer output.