Phase-space volume of regions of trapped motion: multiple ring components and arcs |
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| Authors: | Luis Benet Olivier Merlo |
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| Institution: | (1) Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 48-3, 62251 Cuernavaca, Morelos, Mexico |
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| Abstract: | The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom
respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed
at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances.
The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We
show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate
and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system
as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically
when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume
occupied by the regions of trapped motion. |
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| Keywords: | Phase-space volume of trapped regions Scattering systems Narrow rings Multiple components Ring arcs |
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