Preprint des Projektes: SFB 343: Diskrete Strukturen in der Mathematik

Theorie und Numerik von Aufgaben der linearen Algebra und diskreter dynamischer Systeme

00-051 Gyula Farkas.
Conjugacy in the Discretized Fold Bifurcation

In this paper we construct a conjugacy between the time-1-map of the solution flow generated by an ordinary differential equation and its numerical approximation in a neighborhood of a fold bifurcation point. Our main result is that the conjugacy is O(hp)-close to the identity on the center manifold where h is the step-size and p is the order of the numerical method.