The
talk is devoted to local geometry of distributions (subbundles of
tangent bundles) on manifolds. We will present quite general results on
the finiteness of dimension of symmetry group and on the construction
of the canonical frames for distributions of any rank. One of the
corollaries is that a rank 2 nonholonomic distribution is either the
Goursat distribution (i.e. a distribution locally isomorphic at
generic point to the natural distribution on jet spaces of scalar
functions of one variable) or has finite dimensional algebra of
infinitesimal symmetries. Our method is a combination of ideas
from Optimal Control Theory (a symplectification procedure) and the
generalized Tanaka prolongation procedure for filtered structures on
manifolds.
