Construction of invariant tori around closed orbits

Details Construction of invariant tori around closed orbits Construction of invariant tori around closed orbits

Jul 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995mnras.275..162k&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 275, Issue 1, pp. 162-168.

Astronomy and Astrophysics

Astronomy

7

Celestial Mechanics, Stellar Dynamics, Galaxies: Kinematics And Dynamics

Scientific paper

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 generalized to include motion `trapped' around general closed orbits. This is accomplished by introducing point transformations that map the configuration space around a closed orbit in the target potential to one in a toy potential for which action-angle coordinates are known. This approach 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.

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