The pendulum dilemma of fish orbits

The shape of a galaxy is constrained both by mechanisms of formation (dissipational versus dissipationless) and by the available orbit families (the shape and amount of regular and stochastic orbits). It is shown that, despite the often very flattened shapes of banana and fish orbits, these boxlet orbits generally do not fit a triaxial galaxy in detail because, similar to loop orbits, they spend too little time at the major axis of the model density distribution. This constraint from the shape of fish orbits is relaxed at (large) radii where the density profile of a galaxy is steep.