The geometry of phase mixing

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 space the dimensionality K of which 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 will be stable singularities (catastrophes). The simplest of these are the shells seen in the outer parts of elliptical galaxies.