C. Wulff and F. Schilder.

* Numerical bifurcation of Hamiltonian relative periodic orbits
*

Relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems
and occur for example in celestial mechanics, molecular dynamics and the motion of
rigid bodies. RPOs are solutions which are periodic orbits of the symmetry-reduced system.
In this paper we analyze certain symmetry-breaking
bifurcations of RPOs in Hamiltonian systems with compact symmetry group and
show how they can be detected and computed numerically.
These are turning points of RPOs, relative period-doubling
and relative period-halving bifurcations along branches of RPOs.
In a co-moving frame the latter correspond to symmetry-breaking/symmetry-increasing pitchfork
bifurcations or to period doubling/period-halving bifurcations.

We apply our methods to the family of rotating choreographies
which bifurcate from the famous Figure Eight solution of the three body problem
as angular momentum is varied.
We find that the family of choreographies rotating around the e_2-axis bifurcates
to the family of rotating choreographies that connects to the Lagrange relative equilibrium.
Moreover, we compute several relative period-doubling bifurcations and a turning point
of the family of planar rotating choreographies which bifurcates from the Figure Eight solution
when the third component of the angular momentum vector is varied.