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Riccati equation for two fields of extremals

Speaker: 
M. Zelikin
Institution: 
Steklov Mathematical Institute, Department of Differential Equations
Schedule: 
Monday, December 6, 2004 - 11:00 to 12:00
Location: 
room B
Abstract: 

We consider inplicit differential equations (IDE): F(z,y,p)=0, p=dy/dx, where x belongs to R^1, y,p,f belongs to R^n. Singular points of IDE are points (x,y,p) of the (2n+1)-dimensional space, where F=0 and det(dF/dp)=0, i.e. in such a point it is impossible to reduce IDE to an explicit equation p=(f(x,y). The first part of the lecture is devoted to the case n=1. This is a well-studied problem, the basic construction was invented by H.Poincare`. In this lecture some results of J.Bruce, L.Dara, A.Davydov, F.Tari will be presented. The second part of of the lecture is devoted to the case n>1. This is not so well understood problem (except of the case of quasilinear systems), and we are going to present some recent results.

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