Cosmological dynamics in the model with nonminimal kinetic coupling

Cosmological dynamics has been considered for the FRW Universe filled with a scalar field phi with the kinetic coupling kG(mu nu)phi,(mu)phi,(nu) and the effective potential V (phi) = Vo phi(N). The influence of such potential on the dynamics of the model is found using the methods of the theory of dynamical systems. Two stable asymptotic regimes are obtained: one exists only for 0 < N < 2 and the other one for N > 2. It is also shown that realistic cosmological scenarios are possible in this model.