Maikel Bosschaert, Heinz Hanßmann
Bifurcations in Hamiltonian systems with a reflecting symmetry
(3720K, PostScript (gzipped and uuencoded))
ABSTRACT. A reflecting symmetry q \mapsto -q of a
Hamiltonian system does not leave the symplectic structure
{
m d} q \wedge {
m d } p invariant and is therefore
usually associated with a reversible Hamiltonian system.
However, if q \mapsto -q leads to H \mapsto -H , then
the equations of motion are invariant under the reflection.
Such a symmetry imposes strong restrictions on equilibria
with q = 0 . We study the possible bifurcations triggered
by a zero eigenvalue and describe the simplest bifurcation
triggered by non-zero eigenvalues on the imaginary axis.