On the normal forms for Pfaffian systems.
Hokkaido Mathematical Journal, 35 (2006) pp.815-845
We discuss local normal forms of Pfaffian systems and obtain a necessary and sufficient condition, in terms of relative polarizations, for the local generators of a Pfaffian system to convert to the contact system on the jet manifold $J^r(\R^h,\R^q)$, or to the Pfaffian system associated to a system of partial differential equations. This result generalizes the Darboux theorem on a Pfaffian equation of constant class.
|MSC(Secondary)||58A20, 37J40, 58A17, 37J55|
|Uncontrolled Keywords||Pfaffian system, contact system, relative polarization, local normal form|