Publication Abstracts

Contopoulos 1968

Contopoulos, G., 1968: Resonant periodic orbits. Astrophys. J., 153, 83-94, doi:10.1086/149638.

Resonant periodic orbits, making n oscillations along the x-axis and m oscillations along the y-axis, appear in a two-dimensional potential V = (1/2)(Ax2 + By2) + higher-order terms whenever the ratio A1/2/B1/2 is near n/m. Such orbits can be found by means of a "third" integral in which small divisor terms have been eliminated. Orbits whose initial conditions are near those of a stable resonant periodic orbit are tube orbits. By finding the main periodic orbits, one can derive the main characteristics of the totality of orbits. An application in the case A1/2/B1/2 ≃ 2/3 is given. These considerations can be applied to find the main types of orbits in various galactic models.

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BibTeX Citation

  author={Contopoulos, G.},
  title={Resonant periodic orbits},
  journal={Astrophys. J.},

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RIS Citation

ID  - co03300x
AU  - Contopoulos, G.
PY  - 1968
TI  - Resonant periodic orbits
JA  - Astrophys. J.
VL  - 153
SP  - 83
EP  - 94
DO  - 10.1086/149638
ER  -

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