Asymptotic behavior of N-fields Chiral cosmology

We perform a detailed analysis for the asymptotic behaviour for the multi-scalar field Chiral cosmological scenario. We present the asymptotic behaviour for the one-field, two-fields and three-fields Chiral models. From these results, and deriving conserved quantities, we present a Theorem for the N-fields model for the Chiral model with N-fields. We find that the maximum number of scalar fields which provide interesting physical results at the background level is two-fields, while for N>2 the new stationary points are only of mathematical interest since they do not describe new exact solutions different from those recovered for N=2.