The effects of resonances near corotation in barred galaxies

Studies the effects of higher order resonances in the corotation region. In this region there is an infinity of resonant families of 'simple' periodic orbits closing after one revolution around the center, and n epicyclic oscillations. In the axisymmetric case these families branch off the family of circular periodic orbits x/sub 1/. When a bar is added the resonant families either branch off the (perturbed) family x/sub 1/ (n=odd), or they are produced by breaking the family x/sub 1/ (n=even). There is also an infinity of resonant families of long period orbits around L/sub 4/ and L/sub 5/. The forms of the orbits and of their characteristics are found empirically and they are explained by a non-linear theory based on a (resonant) second integral of motion besides the Jacobi integral. (15 refs).