Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....77..332m&link_type=abstract
Astronomy and Astrophysics, vol. 77, no. 3, Aug. 1979, p. 332-340. Research supported by the Fonds National Suisse de la Recher
Astronomy and Astrophysics
Astrophysics
5
Asymptotic Methods, Dynamic Models, Motion Stability, Orbit Perturbation, Orbital Mechanics, Curves (Geometry), Ergodic Process, Periodic Variations, Potential Fields, Trajectory Analysis
Scientific paper
The relative importance of the third-order terms epsilon and eta in a potential-field expression is investigated in connection with the appearance of instability zones and 'wild' orbital behavior as well as the exact shape of the asymptotic curves emanating from unstable periodic points. The existence and stability of the main periodic orbits are examined, numerical integration is used to sketch the topological evolution of the plane of section in terms of various epsilon and eta values, and some cases of asymptotic curves are calculated. A behavior more complicated than the well-known classical types of asymptotic curve (homoclinic and heteroclinic) is found. A stochasticity criterion inspired by that given by Benettin et al. (1976) is tested and shown to be a useful tool for determining the degree of ergodicity of the system under consideration.
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