Dynamical systems and [sigma]-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 '[sigma]-prolongation'; correspondingly, one has '[sigma]-symmetries' of differential equations. These can be us...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 46; no. 23; pp. 1 - 23
Main Authors Cicogna, G, Gaeta, G, Walcher, S
Format Journal Article
LanguageEnglish
Published 14.06.2013
Subjects
Deformation
Differential equations
Dynamical systems
Fields (mathematics)
Mathematical analysis
Prolongation
Reduction
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Summary: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 1. In this paper, we discuss how [sigma]-symmetries can be used to reduce dynamical systems, i.e. sets of first-order ODEs in the form x super()a= f super()ax).
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/23/235204