Dynamical systems and σ-symmetries

G Cicogna, G Gaeta, S Walcher
2013 Journal of Physics A: Mathematical and Theoretical  
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,
more » ... e. sets of first order ODEs in the form dx^a/dt = f^a (x).
doi:10.1088/1751-8113/46/23/235204 fatcat:2gkingmbejhx5lyh7fhnfm27m4