Critical Cases of 3-DIMENSIONAL Systems

Details Critical Cases of 3-DIMENSIONAL Systems Critical Cases of 3-DIMENSIONAL Systems

Mar 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..42..239c&link_type=abstract

Celestial Mechanics, Volume 42, Issue 1-4, pp. 239-250

Physics

Scientific paper

We study the evolution of families of periodic orbits of simple 3-dimensional models representing the central parts of deformed galaxies. In some cases the evolution is non-unique, i.e. if we follow a closed path in the parameter space we do not return with the same periodic orbit. This happens when the path surrounds a critical point. We found that critical points are generated at particular collisions of bifurcations in limiting cases when the 3-D system is separated into a 2-D system and an independent oscillation along the third axis. The regions of stability and instability of some families of periodic orbits change in remarkable ways near the various collisions of bifurcations and around the critical points.

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