Abstract
There are a number of mathematical theorems in the literature on the dynamics of cosmological models with accelerated expansion driven by a positive cosmological constant Λ or a nonlinear scalar field with potential V (quintessence) which do not assume homogeneity and isotropy from the beginning. The aim of this paper is to generalize these results to the case of k-essence models which are defined by a Lagrangian having a nonlinear dependence on the kinetic energy. In particular, Lagrangians are included where late-time acceleration is driven by the kinetic energy, an effect which is qualitatively different from anything seen in quintessence models. A general criterion for isotropization is derived and used to strengthen known results in the case of quintessence.