Seminar talk, 18 May 2011

Speaker: Rafael Sarkisyan

Title: A remark on the Cartan-Kahler theorem

Abstract:
The talk will discuss an example of algebraic PDE system $R^q \subset J^{q}(X,V)$ and a semi-algebraic set $D^q \subset R^q$ (this set consists of non-involutive points) such that in $D^q$ there are two everywhere dense subsets $A^q$ and $B^q$ having the following property. While for each point $a \in A^q$ it is possible to divide the set of partial derivatives of total order greater than $q$ into parametric and main part (as in the case of involutive points of $R^q$), this is not possible for points of $B^q$. We show how to state correctly an initial value problem for any point $b \in B^q$. This example is related to a question of V.I.Arnold.