  At the classical level anyons with harmonic confinement are known to exhibit
two important properties namely partial separability and pseudo-integrability.
These stem from the fact that this system is locally identical to isotropic
oscillator system but differs in the global topology of the phase space. We
clarify the meaning of pseudo-integrability and show that it amounts to a
definite reduction of the symmetry group. We elaborate on the role of the
fundamental group of the phase space and pseudo-intrgrability in the context of
periodic orbit theory and obtain evidence of non-exactly known eigenvalues from
the semiclassical trace formula. We also discuss an ambiguity regarding the
`half period' trajectories suggested by classical modeling and exhibited by the
exactly known propagator for two anyons.
