Hall motions and star escape in galactic dynamics in the Hill approach

The motion of a galactic cluster is approximately described by those equations in a co-moving frame, introduced by Hill in the XIXth century. Individual motions can only studied numerically, but  for the center of mass interstellar gravitational forces drop out and one is left with a simply system analogous to those considered by Hall for a planar electron in crossed electric and magnetic fields. In both cases, the motion of the COM is  decomposed into bounded oscillations around a guiding center, which follows the Hall law. Translated into a fixed frame yields that most motions escape.

Talk based on:

PM Zhang, G. Gibbons, PAH,
 ``Kohn's theorem and Newton-Hooke symmetry for Hill's eqns,''
Phys. Rev. {\bf D85} (2012) 045031 [arXiv:1112.4793]

PM Zhang et al ,
``Newton-Hooke type symmetry of anisotropic oscillators,''
Ann. Phys. (in press) (2013) [arXiv:1207.2875]