On contact equivalence of systems of ordinary differential equations

2007/12/10 by Wojciech Kryński, Kryński, Wojciech
Mathematics · #34A26 #53A55 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #math.CA #math.DG #msc:34A26 #msc:53A55

paper · pdf · doi:10.48550/arxiv.0712.1455

arxiv created 2009/05/27 · arxiv updated 2009/12/01

Abstract

We consider a problem of equivalence of generic pairs (X,V) on a manifold M, where V is a distribution of rank m and X is a distribution of rank one. We construct a canonical bundle with a canonical frame. We prove that two pairs are equivalent if and only if the corresponding frames are diffeomorphic. As a particular case, with V integrable, we provide a new solution to the problem of contact equivalence of systems of m ordinary differential equations: x^(k+1)=F(t,x,x',...,x^(k)), where k>2 or k=2 and m>1.

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