Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
04-024 Thorsten Hüls.
Bifurcation of Connecting Orbits with One Nonhyperbolic
Fixed Point for Maps
In this paper we consider the bifurcation of transversal
heteroclinic orbits in discrete time dynamical systems. We
assume that a nonhyperbolic transversal heteroclinic orbit
exists at some critical parameter value. This situation appears,
for example, when one end point undergoes a fold or flip
bifurcation. In these two cases the bifurcation analysis of the
orbit is performed in detail. In particular, we prove, using
implicit function techniques, that the orbit can be continued
beyond the bifurcation point. Finally, we show numerical
computations for the fold and for the flip bifurcations.
