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*Boris Doubrov and Boris Komrakov and Tohru Morimoto *

Equivalence of holonomic differential equations

*(Lobachevskii Journal of Mathematics,
Vol.3, pp.39-71)*

Roughly speaking, two differential equations are called equivalent if
one can be transformed into another by a certain change of variables. In
particular, this change of variables transforms solutions of one equation
into solutions of another. Moreover, most methods of solving differential
equations consist of finding a change of variables that will transform
a given equation to a simplier one, for which solutions are known. Thus,
equivalence theory of differential equations underlies most branches in
the theory of differential equations. In this paper we show that for a
large class of differential equations (which, in particular, includes arbitrary
systems of ordinary differential equations) it is possible to answer constructively
to the question, whether two given differential equations are equivalent.
This is achieved by means of transforming this problem into the equivalence
problem for specific geometric structures on smooth manifolds and then
applying powerful techniques of modern differential geometry.

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