  Partially phase-mixed structures in galaxies occupy a complex surface of
dimension D in six-dimensional phase space. The appearance of such structures
to observers is determined by their projection into a subspace whose
dimensionality K is determined by the number of observables (e.g. sky position,
distance, radial velocity, etc.). We discuss the expected dimensionality of
phase-space structures and suggest that the most prominent features in surveys
with K=D or K>D will be stable singularities (catastrophes). The simplest of
these are the shells seen in the outer parts of elliptical galaxies.
