Astronomy and Astrophysics – Astrophysics
Scientific paper
Oct 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...151..279g&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 151, no. 2, Oct. 1985, p. 279-296.
Astronomy and Astrophysics
Astrophysics
31
Elliptical Galaxies, Galactic Rotation, Perturbation Theory, Potential Theory, Stellar Orbits, Stochastic Processes, Astronomical Coordinates, Galactic Evolution, Hamiltonian Functions, Orbital Elements
Scientific paper
While all orbits in an integrable potential are regular, small perturbations of the integrable Hamiltonian in general lead to the appearance of stochastic orbits. This phenomenon can be studied by a technique due to Melnikov. In this paper, a canonically invariant form of Melnikov's method is derived, and the theory is applied to the family of two-dimensional galaxy potentials separable in confocal elliptic coordinates. Under perturbations of these potentials, a stochastic layer forms near the unstable periodic orbit that separates loop and box orbits. The size of this stochastic layer is estimated by the Melnikov integral. For a particular integrable example corresponding to a density proportional to r-2 at large radii, several classes of perturbations are studied.
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