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dc.contributor.authorČap, Andreas
dc.contributor.authorDoubrov, Boris
dc.contributor.authorThe, Dennis
dc.date.accessioned2024-02-26T11:08:07Z
dc.date.available2024-02-26T11:08:07Z
dc.date.issued2023-09-29
dc.description.abstractThe concept of a C-class of differential equations goes back to E. Cartan with the upshot that generic equations in a C-class can be solved without integration. While Cartan’s definition was in terms of differential invariants being first integrals, all results exhibiting C-classes that we are aware of are based on the fact that a canonical Cartan geometry associated to the equations in the class descends to the space of solutions. For sufficiently low orders, these geometries belong to the class of parabolic geometries and the results follow from the general characterization of geometries descending to a twistor space.<p> <p>In this article, we answer the question of whether a canonical Cartan geometry descends to the space of solutions in the remaining cases of scalar ODE of order at least four and of systems of ODE of order at least three. As in the lower order cases, this is characterized by the vanishing of the generalized Wilczynski invariants, which are defined via the linearization at a solution. The canonical Cartan geometries (which are not parabolic geometries) are a slight variation of those available in the literature based on a recent general construction. All the verifications needed to apply this construction for the classes of ODE we study are carried out in the article, which thus also provides a complete alternative proof for the existence of canonical Cartan connections associated to higher order (systems of) ODE.en_US
dc.identifier.citationČap, Doubrov, The. On C-class equations. Communications in analysis and geometry. 2023;30(10):2231-2266en_US
dc.identifier.cristinIDFRIDAID 2195769
dc.identifier.doi10.4310/cag.2022.v30.n10.a2
dc.identifier.issn1019-8385
dc.identifier.issn1944-9992
dc.identifier.urihttps://hdl.handle.net/10037/33037
dc.language.isoengen_US
dc.publisherInternational Pressen_US
dc.relation.journalCommunications in analysis and geometry
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2023 The Author(s)en_US
dc.titleOn C-class equationsen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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