Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
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.
