Stable Chaos in the 12:7 Mean Motion Resonance and Its Relation to the Stickiness Effect

Details Stable Chaos in the 12:7 Mean Motion Resonance and Its Relation to the Stickiness Effect Stable Chaos in the 12:7 Mean Motion Resonance and Its Relation to the Stickiness Effect

Jul 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000icar..146..240t&link_type=abstract

Icarus, Volume 146, Issue 1, pp. 240-252 (2000).

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Scientific paper

We follow the evolution of distributions of real and fictitious asteroids, initially placed in the vicinity of the 12:7 mean motion resonance with Jupiter. Our results show that, besides the well-known example of 522-Helga, other stable chaotic asteroids could, in principle, exist in this region of the belt. Most of the particles, though, attain Jupiter-crossing orbits within 50 Myr, under the influence of other close-by resonances (e.g., 5:3). However, the escape process is also controlled by the initial value of the critical argument ω- ωJ. In this respect 522-Helga can, in fact, be the remnant of a larger initial distribution, as conjectured by M. Murison et al. (1994, Astron. J. 108, 2323-2329). Numerical indications that quasiperiodic orbits exist among the nonremoved test particles support the idea that stable chaos may be a special realization of what is known in Hamiltonian dynamics as stickiness effect. This is also corroborated by the fact that the autocorrelation function, r(k), of the action time series of stable chaotic orbits is almost a quasi-periodic function, in contrast to escaping orbits, for which r(k) decays exponentially. Implications to the problem of formulating a diffusive approach are also discussed.

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