CONSTRUCTION OF INVARIANT TORI AROUND CLOSED ORBITS

The approach and methods introduced by McGill & Binney and Kaasalainen & Binney (Papers I and III), for the construction of phase-space tori that are approximate invariant tori of a given Hamiltonian, are gener alized to include motion 'trapped' around general closed orbits. This is accomplished by introducing point transformations that map the conf iguration space around a closed orbit in the target potential to one i n a toy potential for which action-angle coordinates are known. This a pproach opens up the possibility of constructing tori for an arbitrary orbit family. The method is illustrated by applying it to the 'banana ' and 'fish' minor-orbit families in the planar logarithmic potential.