Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cemda..92..257s&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 92, Issue 1-3, pp. 257-272
Astronomy and Astrophysics
Astronomy
4
Hyperbolic Invariant Sets, Invariant Tori, Stickiness Effect
Scientific paper
With the standard map model, we study the stickiness effect of invariant tori, particularly the role of hyperbolic sets in this effect. The diffusion of orbits originated from the neighborhoods of hyperbolic points, periodic islands and torus is studied. We find that they possess similar diffusion rules, but the diffusion of orbits originated from the neighborhood of a torus is faster than that originated near a hyperbolic set. The numerical results show that an orbit in the neighborhood of a torus spends most of time around hyperbolic invariant sets. We also calculate the areas of islands with different periods. The decay of areas with the periods obeys a power law, and the absolute values of the exponents increase monotonously with the perturbation parameter. According to the results obtained, we conclude that the stickiness effect of tori is caused mainly by the hyperbolic invariant sets near the tori, and the diffusion speed becomes larger when orbits diffuse away from the torus.
Sun Yi-Sui
Zhou Ji-Lin
Zhou Li-Yong
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