  A deformation of the standard prolongation operation, defined on sets of
vector fields in involution rather than on single ones, was recently introduced
and christened "\sigma-prolongation"; correspondingly one has
"\sigma-symmetries" of differential equations. These can be used to reduce the
equations under study, but the general reduction procedure under
\sigma-symmetries fails for equations of order one. In this note we discuss how
\sigma-symmetries can be used to reduce dynamical systems, i.e. sets of first
order ODEs in the form dx^a/dt = f^a (x).
