  The dynamics of a two-qubit system is considered with the aim of a general
categorization of the different ways in which entanglement can disappear in the
course of the evolution, e.g., entanglement sudden death. The dynamics is
described by the function ~n(t), where ~n is the 15-dimensional polarization
vector. This representation is particularly useful because the components of ~n
are direct physical observables, there is a meaningful notion of orthogonality,
and the concurrence C can be computed for any point in the space. We analyze
the topology of the space S of separable states (those having C = 0), and the
often lower-dimensional linear dynamical subspace D that is characteristic of a
specific physical model. This allows us to give a rigorous characterization of
the four possible kinds of entanglement evolution. Which evolution is realized
depends on the dimensionality of D and of D \cap S, the position of the
asymptotic point of the evolution, and whether or not the evolution is
"distance-Markovian", a notion we define. We give several examples to
illustrate the general principles, and to give a method to compute critical
points. We construct a model that shows all four behaviors.
