Abstract
A reflecting symmetry \({q \mapsto -q}\) of a Hamiltonian system does not leave the symplectic structure \({{\rm d}q \wedge {\rm d}p}\) 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.
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Dedicated to Ken Meyer at the occasion of his 75th birthday.
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Bosschaert, M., Hanßmann, H. Bifurcations in Hamiltonian Systems with a Reflecting Symmetry. Qual. Theory Dyn. Syst. 12, 67–87 (2013). https://doi.org/10.1007/s12346-012-0075-z
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DOI: https://doi.org/10.1007/s12346-012-0075-z