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dc.contributor.authorKruglikov, Boris Serafimovich
dc.contributor.authorSchneider, Eivind
dc.date.accessioned2024-03-14T14:11:44Z
dc.date.available2024-03-14T14:11:44Z
dc.date.issued2023
dc.description.abstractWe observe that, up to conjugation, a majority of higher order ODEs (ordinary differential equations) and ODE systems have only fiber-preserving point symmetries. By exploiting Lie's classification of Lie algebras of vector fields, we describe all exceptions to this in the case of scalar ODEs and systems of ODEs on a pair of functions. The scalar ODEs whose symmetry algebras are not fiber preserving can be expressed via absolute and relative scalar differential invariants, while a similar description for ODE systems requires us to also invoke conditional differential invariants and vector-valued relative invariants to deal with singular orbits of the action. Investigating prolongations of the actions, we observe some interesting relations between different realizations of Lie algebras. We also note that it may happen that the prolongation of a finite-dimensional Lie algebra acting on a differential equation never becomes free. An example of an underdetermined ODE system for which this phenomenon occurs shows limitations of the method of moving frames.en_US
dc.descriptionSource at <a href=https://www.heldermann.de/JLT/JLT33/JLT334/jlt33048.htm>https://www.heldermann.de/JLT/JLT33/JLT334/jlt33048.htm</a>.en_US
dc.identifier.citationKruglikov BS, Schneider E. ODEs whose Symmetry Groups are not Fiber-Preserving. Journal of Lie theory. 2023;33(4):1045-1086en_US
dc.identifier.cristinIDFRIDAID 2222656
dc.identifier.doi10.48550/arXiv.2202.10331
dc.identifier.issn0949-5932
dc.identifier.urihttps://hdl.handle.net/10037/33166
dc.language.isoengen_US
dc.publisherHeldermann Verlagen_US
dc.relation.journalJournal of Lie theory
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2023 The Author(s)en_US
dc.titleODEs whose Symmetry Groups are not Fiber-Preservingen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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