Dynamical systems and \sigma-symmetries
Mathematical Physics
2013-05-29 v1 Dynamical Systems
math.MP
Abstract
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).
Cite
@article{arxiv.1305.6331,
title = {Dynamical systems and \sigma-symmetries},
author = {Giampaolo Cicogna and Giuseppe Gaeta and Sebastian Walcher},
journal= {arXiv preprint arXiv:1305.6331},
year = {2013}
}