 11138 Maikel Bosschaert, Heinz Hanßmann
 Bifurcations in Hamiltonian systems with a reflecting symmetry
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Oct 3, 11

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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 nonzero eigenvalues on the imaginary axis.
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