Resonant Periodic Orbits
Abstract
Resonant periodic orbits, making n oscillations along the xaxis and m oscillations along the yaxis, appear in a twodimensional potential V = ~(Ax2 + By2) + higherorder terms whenever the ratio A1/2/B'12 is near n/rn. 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 A'12/B1/2 ~ is given. These considerations can be applied to find the main types of orbits in various galactic models
 Publication:

The Astrophysical Journal
 Pub Date:
 July 1968
 DOI:
 10.1086/149638
 Bibcode:
 1968ApJ...153...83C