Stable Chaos in the 12:7 Mean Motion Resonance and Its Relation to the Stickiness Effect
✍ Scribed by Kleomenis Tsiganis; Harry Varvoglis; John D Hadjidemetriou
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 390 KB
- Volume
- 146
- Category
- Article
- ISSN
- 0019-1035
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✦ Synopsis
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 -J . 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.