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## higher order structure by higher order derivatives

Anyone recall a structure determined by a 3rd order partial derivative? not the general nth order of recent Baranovsky

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 I don't understand the question. What does "structure determined by a 3rd order partial" mean? – Hans Stricker Jul 23 2011 at 14:49 Have you considered having a look at math.stackexchange.com/questions/14841 ? Or else, to repeat the question of Hans: what is your question? – András Bátkai Jul 23 2011 at 19:33 Just in case (but I am to far from this topic): a foliated $3$-web in the plane is linearizable if and only if its curvature is $\equiv0$. Isn't true that this curvature involves the third derivatives of the vector field defining the foliations ? – Denis Serre Jul 23 2011 at 19:56