Reduction to finite dimensions of continuous systems having only a few amplified modes

2008

In the approach of Guckenheimer and Knobloch the amplitudes of trajectories on the unstable manifold 0 are the pivotal quantities. This places a certain restriction on the applicability of this approach, as only neighbourhoods of 0 of the unstable manifold of 0 are accessible, which have a one-to-one projection into their tangent at 0, the linear space spanned by the amplified modes. This restriction may be lifted, using the arc lengths of trajectories instead.