Bianca Thiere
University of Paderborn
Department of Mathematics and Computer Science
University of Paderborn
D-33095 Paderborn
thiere@math.uni-paderborn.de
Abstract:
We propose a new method for the numerical detection of
connecting orbits. This method is based on numerical tools
for the set-wise approximation of invariant manifolds.
Applying the hat algorithm to a parameter dependent
dynamical system we are looking for an intersection of
coverings of the stable manifold of one fixed point and
the unstable manifold of another one while varying the
parameter. As a result we do not just get an approximation
of the parameter value for which a connecting orbit
exists but also a good estimate on the location of this
orbit which can then be used as an initial guess for its
direct computation.