Abstract
We present the analysis of the bifurcation sequences of a family of resonant 2-DOF Hamiltonian systems invariant under spatial mirror symmetry and time reversion. The phase-space structure is investigated by a singularity theory approach based on the construction of a universal deformation of the detuned Birkhoff–Gustavson normal form. Thresholds for the bifurcations of periodic orbits in generic position are computed as asymptotic series in terms of physical parameters of the original system.
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Acknowledgments
We acknowledge useful discussions with C. Efthymiopoulos, H. Hanßmann, G. Gaeta and F. Verhulst. A. M. is supported by the European social fund “Support of inter-sectoral mobility and quality enhancement of research teams at Czech Technical University in Prague” (CZ.1.07/2.3.00/30.0034). G. P. is partially supported by INFN, Sezione di Roma Tor Vergata, by the European MC-ITN Grant “Stardust” and by GNFM-INdAM.
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Marchesiello, A., Pucacco, G. Universal unfolding of symmetric resonances. Celest Mech Dyn Astr 119, 357–368 (2014). https://doi.org/10.1007/s10569-014-9557-4
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DOI: https://doi.org/10.1007/s10569-014-9557-4