  A novel method for the calculation of eigenfrequencies of non-uniformly
filled spherical cavity resonators is developed. The impact of the system
symmetry on the electromagnetic field distribution as well as on its degrees of
freedom (the set of resonant modes) is examined. It is shown that in the case
of angularly symmetric cavity, regardless of its radial non-uniformity, the set
of resonator modes is, as anticipated, a superposition of TE and TM
oscillations which can be described in terms of a single scalar function
independently of each other. The spectrum is basically determined through the
introduction of effective ``dynamic'' potentials which encode the infill
inhomogeneity. The violation of polar symmetry in the infill dielectric
properties, the azimuthal symmetry being simultaneously preserved, suppresses
all azimuthally non-uniform modes of electric-type (TM) oscillations. In the
absence of angular symmetry of both electric and magnetic properties of the
resonator infill, only azimuthally uniform distribution of both TM and TE
fields is expected to occur in the resonator. The comparison is made of the
results obtained through the proposed method and of the test problem solution
obtained with use of commercial solvers. The method appears to be efficient for
computational complex algorithms for solving spectral problems, including those
for studying the chaotic properties of electrodynamic systems' spectra.
