Dynamics of $k$-essence
  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 $\Lambda$ 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. 
Alan D. Rendall