Preprint des Projektes: DFG Forschergruppe Spektrale Analysis, asymptotische Verteilungen und stochastische Prozesse

Numerische Approximation und Spektrale Analysis unendlich-dimensionaler Dynamischer Systeme

03-006 Lajos Loczi.
A normal form for the fold bifurcation and its discretization

In the first part of the paper, normal forms for the time-h-map of an ordinary differential equation and its discretization near a fold bifurcation point in one dimension are derived together with suitable closeness estimates. These steps will pave the way for an anticipated generalization of the results for the time-1-flow by G. Farkas (2002). The second, complementary part of the paper shows that implicit Runge-Kutta methods completely preserve the fold as well as the cusp bifurcation conditions in N dimension.