Resonances and bifurcations in axisymmetric scale-free potentials |
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| Authors: | Giuseppe Pucacco |
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| Institution: | Physics Department, University of Rome 'Tor Vergata', Via della Ricerca Scientifica, 1 I00133 Rome, Italy;INFN, Sezione Roma Tor Vergata, Via della Ricerca Scientifica, 1 I00133 Rome, Italy |
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| Abstract: | We investigate an analytical treatment of bifurcations of families of resonant 'thin' tubes in axisymmetric galactic potentials. We verify that the most relevant bifurcations are due to the (1:1) resonance producing the 'inclined' orbits through two different mechanisms: from the disc orbit and from the 'thin' tube associated with the vertical oscillation. The closest resonances occurring after these are the (4:3) resonance in the oblate case and the (2:1) resonance in the prolate case. The (1:1) resonances are treated in a straightforward way using a second-order truncated normal form. The higher order resonances are instead cumbersome to investigate, because the normal form has to be truncated to a high degree and the number of terms grows very rapidly. We therefore adopt a further simplification giving analytical formulae for the values of the parameters at which bifurcations ensue and compare them with selected numerical results. Thanks to the asymptotic nature of the series involved, the predictions are reliable well beyond the convergence radius of the original series. |
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| Keywords: | methods: analytical galaxies: kinematics and dynamics |
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