Mathematics
Scientific paper
Mar 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984a%26a...132..381m&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 132, no. 2, March 1984, p. 381-384.
Mathematics
7
Barred Galaxies, Galactic Rotation, Galactic Structure, Branching (Mathematics), Orbital Mechanics, Resonance
Scientific paper
The condition of appearance of the 1/1 resonance whose corresponding condition is closed inside corotation in SB galaxies is clarified. It is shown that the relation between the appearance of the so-called bubbles and the value of parameters characterizing the strength of the bar is demonstrated. The effect of the resonance on the shape and stability of the main direct family of periodic orbits is described. In general, the bifurcation of this family into the 1/1 resonant family of symmetric periodic orbits almost always exists jointly with another bifurcation of an asymmetrical 1/1 family whose orbits have a figure eight shape similar to those found by Miller and Smith (1979) in N-body simulations. The possibility of real galaxies existing with 1/1 resonance present in them is examined.
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