Topics in numerical linear algebra and discrete dynamical systems
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.
