Hokkaido Mathematical Journal

HONDA Tomomi,

On the normal forms for Pfaffian systems.

Hokkaido Mathematical Journal, 35 (2006) pp.815-845

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Abstract

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(Primary)70H07
MSC(Secondary)58A20, 37J40, 58A17, 37J55
Uncontrolled KeywordsPfaffian system, contact system, relative polarization, local normal form