Dynamical systems and σ-symmetries

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 "σ-prolongation"; correspondingly one has "σ-symmetries" of differential equations. These can be used to reduce the equations under study, but the general reduction procedure under σ-symmetries fails for equations of order one. In this note we discuss how σ-symmetries can be used to reduce dynamical systems, i.e. sets of first order ODEs in the form dx^a/dt = f^a (x).

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