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Valeriy Yumaguzhin

Publications and source records attributed to Valeriy Yumaguzhin.

6 recordsLinked to original sources
arXiv2023

On invariants and equivalence of differential operators under Lie pseudogroups actions

In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and solve the equivalence problem for actions of algebraic Lie pseudogroups. As a running example of application of the methods, we use the pseudogroup of local symplectomorphisms.

math.DG↗
arXiv2022

On natural invariants and equivalence of differential operators

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order $k\ge 2$ on a smooth manifold of dimension $n\ge 2$ and show their application to the equivalence problem of such operators.

math.DG↗
arXiv2020

Invariants of forth order linear differential operators

In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.

math.DG↗