Семинар по маломерной математике
Пятница, 18 апреля 2008, $16^{00}-17^{45}$, ауд. 311

В.М.Закалюкин (Москва--Ливерпуль)
Lagrangian projections with boundary.

We consider Lagrangian mappings  of a Lagrangian manifold with a
boundary. A boundary is an isotropic hypersurface in the
Lagrangian manifold. These pairs are natural in various settings
of singularity theory applications to differential equations and
variational problems. Isotropic submanifold plays the role of the
initial data set and Lagrangian submanifold is the solution of   
Hamilton-Jacobi equation with the initial data.

The pair is embedded into the phase space which usually is the
cotangent bundle  of the configuration space. We  classify simple
classes of the projections to the configuration space of these   
pairs.

As it is well known the  Arnold's boundary singularities  are 
related to  projections of the  pairs of Lagrangian submanifolds 
(of dimension $n$) which has $n-1$-dimensional regular 
intersection and transversal complementary directions.  We use 
more rough equivalence relation of the  corresponding generating 
families. 

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