The geometry of phase mixing

Partially phase-mixed structures in galaxies occupy a complex surface of di mension D in six-dimensional phase space. The appearance of such structures to observers is determined by their projection into a space the dimensiona lity K of which is determined by the number of observables (e.g. sky positi on, distance, radial velocity, etc.). We discuss the expected dimensionalit y of phase-space structures and suggest that the most prominent features in surveys with K greater than or equal to D will be stable singularities (ca tastrophes). The simplest of these are the shells seen in the outer parts o f elliptical galaxies.