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C. Hunter (Florida State University)
Building galactic models requires the use of a large number of orbits, and so is helped by rapid ways of obtaining accurate descriptions of them. Regular orbits lie on 3-tori in phase space, are quasi-periodic with three fundamental frequencies, and can be described by triple Fourier series. The triple Fourier series are strongly constrained by the Hamiltonian nature of the problem, because they are derivable from the scalar generating function which gives the canonical transformation to action-angle variables. Orbital symmetries are reflected in the special structure of their Fourier series. This talk will discuss efficient ways of using all the phase space information available from numerical integrations of orbits to derive their Fourier series. Once the Fourier series are known, orbital densities can be derived directly from them (Copin, Zhao, & de Zeeuw 2000).
This work has been supported by NSF through grant DMS-9704615.