  The background dynamical evolution of a universe filled with matter and a
cosmological scalar field is analyzed employing dynamical system techniques.
After the phenomenology of a canonical scalar field with exponential potential
is revised, square and square root kinetic corrections to the scalar field
canonical Lagrangian are considered and the resulting dynamics at cosmological
distances is obtained and studied. These noncanonical cosmological models imply
new interesting phenomenology including early time matter dominated solutions,
cosmological scaling solutions and late time phantom dominated solutions with
dynamical crossing of the phantom barrier. Stability and viability issues for
these scalar fields are presented and discussed.
