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arXiv · 1305.6331

Dynamical systems and \sigma-symmetries

Giampaolo Cicogna·Giuseppe Gaeta·Sebastian Walcher
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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).

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Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher. 2013-05-27. Dynamical systems and \sigma-symmetries. https://doi.org/10.1088/1751-8113/46/23/235204

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