Cosmological dynamics of scalar fields with kinetic corrections: Beyond the exponential potential

We expand the dynamical systems investigation of cosmological scalar fields characterised by kinetic corrections presented in [N. Tamanini, Phys. Rev. D 89 (2014) 083521]. In particular we do not restrict the analysis to exponential potentials only, but we consider arbitrary scalar field potentials and derive general results regarding the corresponding cosmological dynamics. Two specific potentials are then used as examples to show how these models can be employed not only to describe dark energy, but also to achieve dynamical crossing of the phantom barrier at late times. Stability and viability issues at the classical level are also discussed.