Abstract
Let V be a vector field distribution or Pfaffian system on manifold M. We give an efficient algorithm for the construction of local coordinates on M such that V may be locally expressed as some partial prolongation of the contact distribution C(1)q, on the first-order jet bundle of maps from ℝ to ℝq, q ≥ 1. It is proven that if V is locally equivalent to a partial prolongation of C(1)q, then the explicit construction of contact coordinates algorithmically depends upon the determination of certain first integrals in a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on M. The number of these first integrals that must be computed satisfies a natural minimality criterion. These results provide a full and constructive generalisation of the Goursat normal form from the theory of exterior differential systems.
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Vassiliou, P. Efficient Construction of Contact Coordinates for Partial Prolongations. Found Comput Math 6, 269–308 (2006). https://doi.org/10.1007/s10208-004-0148-8
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DOI: https://doi.org/10.1007/s10208-004-0148-8