C. Wulff, F. Schilder.

* Relative Lyapunov Centre Bifurcations
*

Relative equilibria and relative periodic orbits (RPOs)
are ubiquitous in symmetric Hamiltonian systems
and occur for example in celestial mechanics, molecular dynamics and rigid body
motion. Relative equilibria are equilibria and RPOs
are periodic orbits in the symmetry
reduced system.
Relative Lyapunov centre bifurcations are bifurcations of relative periodic orbits
from relative equilibria corresponding to Lyapunov centre bifurcations of the symmetry
reduced dynamics.
In this paper we first prove a relative Lyapunov centre theorem by combining
recent results on persistence of RPOs in Hamiltonian systems with a symmetric
Lyapunov centre theorem of Montaldi et al.
We then develop numerical methods for the detection of
relative Lyapunov centre bifurcations along branches of RPOs and for their computation.
We apply our methods to Lagrangian relative equilibria of the N
body problem.