Abstract
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 KD will be stable singularities (catastrophes). The simplest of these are the shells seen in the outer parts of elliptical galaxies.
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