A constructive generalised Goursat normal form

2004/04/21 by Peter J. Vassiliou, Vassiliou, Peter J. · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.DG #msc:58J60

paper · pdf · doi:10.48550/arxiv.math/0404377

33 pages

arxiv created 2004/04/21 · arxiv updated 2009/12/01

Abstract

We provide necessary and sufficient conditions on the derived type of a vector field distribution \Cal V in order that it be locally equivalent to a partial prolongation of the contact distribution \Cal C⁽¹⁾_q, on the first order jet bundle of maps from \Bbb R to \Bbb R^q, q≥ 1. This result fully generalises the classical Goursat normal form. Our proof is constructive: it is proven that if \Cal V is locally equivalent to a partial prolongation of \Cal C⁽¹⁾_q then the explicit construction of contact coordinates algorithmically depends upon the integration of a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on the ambient manifold.

Cited by

• Quotients of Invariant Control Systems

Related

• Efficient construction of contact coordinates for partial prolongations
• Contact systems and corank one involutive subdistributions
• Small growth vectors of the compactifications of the contact systems on J ^r(1,1)
• On the geometry of Goursat structures
• Novel pathways in k-contact geometry