C. Wulff.

* A Hamiltonian analogue of the meandering transition *

In this paper we present a
Hamiltonian analogue of the well-known meandering transition
from rotating waves to modulated
rotating and modulated travelling waves in systems
with Euclidean symmetry. In dissipative systems, in particular in
spiral wave dynamics, this
transition is caused
by varying external parameters such that
a Hopf bifurcation in a corotating frame occurs.
In the Hamiltonian case, for example in models of point vortex dynamics,
the conserved quantities of the system,
angular and linear momentum, are bifurcation parameters.
We prove that, depending on the symmetry properties of the momentum map,
either modulated traveling waves do not occur at all, or that, in contrast to the
dissipative case, modulated traveling waves are the typical scenario near rotating
waves in momentum parameter space.
We also treat systems with the symmetry group of a sphere and with
the Euclidean symmetry group of rotations and translations in three-dimensional space.