  We investigate the planar anisotropic harmonic oscillator with explicit
rotational symmetry as a particle model with non-commutative coordinates. It
includes the exotic Newton-Hooke particle and the non-commutative Landau
problem as special, isotropic and maximally anisotropic, cases. The system is
described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the
isotropic case, and develops three different phases depending on the values of
the two central charges. The special cases of the exotic Newton-Hooke particle
and non-commutative Landau problem are shown to be characterized by additional,
so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral
properties.
