The agenda of next meetings of Krasil'shchik's seminar on geometry of
differential equations at the Independent University of Moscow.

On 23 February the seminar meets offline in room 303 of the Independent
University of Moscow, on 19:20 MSK as usual, simultaneously, there will
be broadcast via Zoom.

Speaker: Boris Kruglikov
Title: ODEs with essential contact or point symmetries
Language: English
Zoom:
https://us06web.zoom.us/j/8817121842?pwd=TWpEMFlTellyMGpuV09LbkY2NUdnUT09
Zoom Passcode: 3075

Abstract:

(joint work with Eivind Schneider)

We observe that, up to conjugation, a majority of higher order ODEs and
ODE systems have only point fiber-preserving symmetries (surprisingly
this is also true for "most interesting" ODEs). We describe all the
exceptions in the case of scalar ODEs and systems of pairs of ODEs on a
pair of functions. We exploit classifications of Lie algebras of vector
fields in 2 and 3 dimensions.

While we can express scalar ODEs with essentially contact or point
symmetry algebras via absolute and relative differential invariants, we
have to invoke also conditional differential invariants in the case of
ODE systems 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.

Investigating prolongations of the actions, we observe some interesting
relation s between different realizations of Lie algebras. We also note
that prolongation of a finite-dimensional Lie algebra acting on a
differential equation may not eventually become free. An example of
underdetermined ODE with this phenomenon shows limitations of the method
of moving frames.


The seminar meets on Wednesday evenings at 19:20 MSK in room 303
and in Zoom, Meeting ID: 88 17 12 1842
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FROM 129.151.90.*