Abstract
We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical system, such as the mass and the scale length of the nucleus, the angular momentum or the energy, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. Some heuristic arguments to explain and justify the numerically derived outcomes are also given. Furthermore, we present a new method to find the threshold between chaos and regularity for both Lyapunov Characteristic Numbers and SALI, by using them simultaneously.
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Notes
We adhere to the recommended IAU symbol for year, i.e., “a” (Wilkins 1989).
A regular orbit of a \(N\)-dimensional potential obeys, by definition, \(N\) or more isolating integrals of motion. On the other hand, a chaotic orbit is defined through its sensitivity to the initial conditions in phase space: if the initial conditions of the orbit are infinitesimally displaced, then the distance between the original orbit and the new orbit grows exponentially with time. These definitions do not complement each other. Whereas it can be proved that a regular orbit is not chaotic and a chaotic orbit is not regular (e.g., Jackson 1991 Section 8.3), as far as we know it has not been proved that every irregular (i.e. not regular) orbit is chaotic, or, in other words, that every orbit obeying less than \(N\) isolating integrals has sensitivity to the initial conditions. Nevertheless, to avoid confusion, we will follow here the widespread convention of considering irregular orbits and chaotic orbits as the same set.
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Acknowledgments
The authors would like to thank the anonymous referee for the careful reading of the manuscript and for all the aptly suggestions and comments which allowed us to improve both the quality and the clarity of our work. This work was supported with grants from the Universidad Nacional de La Plata (Argentina), the Consejo Nacional de Investigaciones Cientí ficas y Técnicas de la República Argentina, and the Agencia Nacional de Promoción Científica y Tecnológica (Argentina).
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Zotos, E.E., Carpintero, D.D. Orbit classification in the meridional plane of a disk galaxy model with a spherical nucleus. Celest Mech Dyn Astr 116, 417–438 (2013). https://doi.org/10.1007/s10569-013-9500-0
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DOI: https://doi.org/10.1007/s10569-013-9500-0