BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway) DTSTART:20220223T162000Z DTEND:20220223T180000Z DTSTAMP:20260423T024832Z UID:GDEq/57 DESCRIPTION:Title: OD Es with essential contact or point symmetries\nby Boris Kruglikov (UiT the Arctic University of Norway) as part of Geometry of differential equa tions seminar\n\nLecture held in room 303 of the Independent University of Moscow.\n\nAbstract\n(joint work with Eivind Schneider)\n\nWe observe tha t\, up to conjugation\, a majority of higher order ODEs and ODE systems ha ve only point fiber-preserving symmetries (surprisingly this is also true for "most interesting" ODEs). We describe all the exceptions in the case o f scal ar ODEs and systems of pairs of ODEs on a pair of functions. We exp loit classifications of Lie algebras of vector fields in 2 and 3 dimension s.\n\nWhile we can express scalar ODEs with essentially contact or point s ymmetry algebras via absolute and relative differential invariants\, we ha ve to invoke also conditional differential invariants in the case of ODE s ystems to deal with singular orbits of the action. In the scalar case the result is partially due to Lie\, but we consider the global classification and discuss the algebra of relative invariants. For systems the result is new.\n\nInvestigating prolongations of the actions\, we observe some inte resting relations between different realizations of Lie algebras. We also note that prolongation of a finite-dimensional Lie algebra acting on a dif ferential equation may not eventually become free. An example of underdete rmined ODE with this phenomenon shows limitations of the method of moving frames.\n LOCATION:https://researchseminars.org/talk/GDEq/57/ END:VEVENT END:VCALENDAR