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SUMMARY:Boris Doubrov
DTSTART:20211124T162000Z
DTEND:20211124T180000Z
DTSTAMP:20260423T022056Z
UID:GDEq/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/49/">On
  Cartan's C-class differential equations</a>\nby Boris Doubrov as part of 
 Geometry of differential equations seminar\n\nLecture held in room 303 of 
 the Independent University of Moscow.\n\nAbstract\nWe consider a very spec
 ial class of differential equations\, which is characterized by the condit
 ion that all its local differential invariants (under the action of a suit
 able Lie pseudogroup) become first integrals when restricted to the equati
 on manifold. Such differential equations were introduced in a short note o
 f Elie Cartan (Les espaces généralisés et l'intégration de certaines c
 lasses d'équations différentielles\, C.R.\, 1938\, V.206\, N.23\, 1689-1
 693)\, who characterized them in two simplest cases: scalar 2nd order ODEs
  viewed under the pseudogroup of point transformations and scalar 3rd orde
 r ODEs under the group of contact transformations. We show how these resul
 ts generalize to any systems of ODEs and\, more generally\, differential e
 quations of finite type. The same question for arbitrary systems of PDEs s
 till remains open.\n
LOCATION:https://researchseminars.org/talk/GDEq/49/
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